Factors of 24

The factor pairs of 24 are: 1 x 24, 2 x 12, 3 x 8, and 4 x 6. When you find the factors of a number, you are looking for numbers that can be multiplied together to get that number. Notice that the...Prime factors of 24 : 2x2x2, 3. In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicities; the process of determining these factors is called integer factorization.This calculator factors a set of positive integers to find the common factors (common divisors) of those integers. Enter the set of numbers you want to factor separating them with commas. Click "Calculate" to see all factors of each number as well as the greatest common factor (GCF). The factors of a number include all divisors of that number. Jul 24, 2007 · Results. Of 7100 cooks, 5835 (82%) replied to the questionnaire, including 1010 men and 4825 women. The mean age was 41.4 for men and 47.5 for women. Prime Factors Calculator. The number 24 is a composite number because 24 can be divided by one, by itself and at least by 2 and 3. A composite number is an integer that can be divided by at least another natural number, besides itself and 1, without leaving a remainder (divided exactly). The factorization or decomposition of 24 = 2 3 •3.The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Now, to find the greatest common factor, we find the largest number that is on both lists. This number is 8. What's the GCF of 32 and 40? The GCF of 32 and 40 is 8.24 ÷ 2 = 12. 24 ÷ 2=12. This results in a whole number, so you can continue dividing by 2. 12 ÷ 2 = 6. 6 ÷ 2 = 3. 3 ÷ 2 = 1.5. This is not a whole number, so instead, try dividing by the next smallest prime factor 3. 3 ÷ 3 = 1. The result has reached 1, so all the prime factors needed to express 24 have been found.As we know factors of 24 are all the numbers that can exactly divide the number 24 simply divide 24 by all the numbers up to 24 to see the ones that result in zero remainders. Numbers that divide without remainder are factors and in this case below are the factors Factors of 24 Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Now understand the basic concept of factor and how to find the factors in easy way. What is the factor? Factors are integers you multiply together to get another integer. Also remember that the factors always include 1 and itself. indeed jobs cape girardeau mo The factors of 24 are all of the factors of 24 that multiply together to equal twenty-four.Factors of 24 equal 1,2,3,4,6,8,12.24Prime factors of 24 equal 2,2...The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors. The number of prime factors of 24 is 2. Factor tree or prime decomposition for 24 As 24 is a composite number, we can draw its factor tree:GCF of 15 and 24 is the largest possible number that divides 15 and 24 exactly without any remainder. The factors of 15 and 24 are 1, 3, 5, 15 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 15 and 24 - Euclidean algorithm, long division, and prime factorization. What is GCF of 15 and 24?Oct 13, 2021 · Number of factors of 24 The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore the total number of factors of 24 is eight. Prime Factors of 24 We have found above that the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors. Here is the complete solution of finding Prime Factors of 24: The smallest Prime Number which can divide 24 without a remainder is 2. So the first calculation step would look like: 24 ÷ 2 = 12. Now we repeat this action until the result equals 1: 12 ÷ 2 = 6. 6 ÷ 2 = 3. 3 ÷ 3 = 1. The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors. The number of prime factors of 24 is 2. Factor tree or prime decomposition for 24 As 24 is a composite number, we can draw its factor tree:Sep 21, 2022 · The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and its negative factors are -1, -2, -3, -4, -6, -8, -12, -24. What is a prime factor of 24? Factors of 24 are basically the numbers that divide it evenly or exactly without leaving any remainder i.e if a number divides 24 with a remainder of zero, then that number is called a factor. The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors. The number of prime factors of 24 is 2. Factor tree or prime decomposition for 24 As 24 is a composite number, we can draw its factor tree: Factoring Calculator gives Factors of 24 i.e. 1, 2, 3, 4, 6, 8, 12, 24 numbers that divide 24 without a remainder. Find a factor tree of 24 easily with this online tool. 24 ÷ 2 = 12. 24 ÷ 2=12. This results in a whole number, so you can continue dividing by 2. 12 ÷ 2 = 6. 6 ÷ 2 = 3. 3 ÷ 2 = 1.5. This is not a whole number, so instead, try dividing by the next smallest prime factor 3. 3 ÷ 3 = 1. The result has reached 1, so all the prime factors needed to express 24 have been found.The second method to find GCF for numbers 24 and 32 is to list all Prime Factors for both numbers and multiply the common ones: All Prime Factors of 24 : 2, 2, 2, 3 All Prime Factors of 32 : 2, 2, 2, 2, 2Jul 24, 2007 · Results. Of 7100 cooks, 5835 (82%) replied to the questionnaire, including 1010 men and 4825 women. The mean age was 41.4 for men and 47.5 for women. Oct 13, 2021 · At first, we will find the factors of 24 by the multiplication method. In this method, we need to write the number 24 multiplicatively in all possible ways. We have: 24 = 1×24. ∴ 1, 24 are factors of 24. 24 = 2×12. ∴ 2,12 are factors of 24. 24 = 3×8. ∴ 3, 8 are factors of 24. What is the factors of 24? There are a total of eight factors of 24, they are 1, 2, 3, 4, 6, 8, 12 and 24. Pair factors of 24 are the numbers, which gives the pegboard home depot All Prime Factors of 24 : 2, 2, 2, 3 As we can see there is only one Prime Factor common to both numbers. It is 2 So 2 is the Greatest Common Factor of 10 and 24 Print List of positive integer factors of 24 that divides 24 without a remainder. 1, 2, 3, 4, 6, 8, 12, 24 Greatest Common Factor We found the factors of 24 . The biggest common factor number is the GCF number. So the Greatest Common Factor 24 is 24. Therefore, GCF of numbers 24 is 24 Finding GCF of 24 using Prime Factorization Given Input Data is 24A factor tree can be used to determine the prime factors of 24, as shown in the figure. From the factor tree, we can see that the prime factorization of 24 is 2 × 2 × 2 × 3. This means 2 and 3 are the only prime factors of 24. Factor Pairs of 24. The factor pair of any number is a set of two integers that, when multiplied, result in that number.Feb 08, 2010 · The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.The prime factors of 24 are: 2 and 3.The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40.The prime factors of 40 ... 7 hours ago · Ahmed Bahaa, an Egyptian national, stated that, “Warranty was one of the most important factors that helped me confirm my decision to buy a car from CARS24. I strongly believe that without a... How many common factors are there in 12, 24 and 36? A.4 B. 5 C.6 D.7. Answers: 2 Get Iba pang mga katanungan: Math. Math, 28.10.2019 16:29, girly61. 2.at the start of ... What are the factors of 24? Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. 3. How do you factor 24 on a calculator? All you have to do is provide the input value 24 and tap on the enter button next to the input field to obtain the factors. Apr 19, 2021 · includes one and itself so the factor of 24 will be 1, and itself that is 24. The simple way to find factors means what pairs of number multiply to get 24 that is if you multiply 1 times 20 foot then you will get 24 if you divide this 24 by 1 then you will get 24 and if you divide this beautiful by this 24 you The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors. The number of prime factors of 24 is 2. Factor tree or prime decomposition for 24 As 24 is a composite number, we can draw its factor tree: adidas romper As we know factors of 24 are all the numbers that can exactly divide the number 24 simply divide 24 by all the numbers up to 24 to see the ones that result in zero remainders. Numbers that divide without remainder are factors and in this case below are the factors Feb 08, 2010 · The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.The prime factors of 24 are: 2 and 3.The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40.The prime factors of 40 ... Factor out the GCF. 24 a_{2}-36 a-12Watch the full video at:https://www.numerade.com/questions/factor-out-the-gcf-24-a_2-36-a-12/Never get lost on homework a...Factoring Calculator gives Factors of 24 i.e. 1, 2, 3, 4, 6, 8, 12, 24 numbers that divide 24 without a remainder. Find a factor tree of 24 easily with this online tool.Factor out the GCF. 24 a_{2}-36 a-12Watch the full video at:https://www.numerade.com/questions/factor-out-the-gcf-24-a_2-36-a-12/Never get lost on homework a... Jul 19, 2022 · A factor is a number that goes into another number exactly. For example, 10 is a factor of 100 because 100 can be divided by 10. Factors of 24 refer to the numbers that can exactly divide 24 leaving the remainder 0. Oct 13, 2021 · At first, we will find the factors of 24 by the multiplication method. In this method, we need to write the number 24 multiplicatively in all possible ways. We have: 24 = 1×24. ∴ 1, 24 are factors of 24. 24 = 2×12. ∴ 2,12 are factors of 24. 24 = 3×8. ∴ 3, 8 are factors of 24. Jul 19, 2022 · A factor is a number that goes into another number exactly. For example, 10 is a factor of 100 because 100 can be divided by 10. Factors of 24 refer to the numbers that can exactly divide 24 leaving the remainder 0. how to forward a text Jul 19, 2022 · A factor is a number that goes into another number exactly. For example, 10 is a factor of 100 because 100 can be divided by 10. Factors of 24 refer to the numbers that can exactly divide 24 leaving the remainder 0. GCF of 15 and 24 is the largest possible number that divides 15 and 24 exactly without any remainder. The factors of 15 and 24 are 1, 3, 5, 15 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 15 and 24 - Euclidean algorithm, long division, and prime factorization. What is GCF of 15 and 24?As we know factors of 24 are all the numbers that can exactly divide the number 24 simply divide 24 by all the numbers up to 24 to see the ones that result in zero remainders. Numbers that divide without remainder are factors and in this case below are the factors Sep 29, 2022 · Divide 24 with its smallest prime factor. Here, the smallest prime factor of 24 is 2. So, 24 ÷ 2 = 12. Repeated division of obtained quotient by 2 until we get a number that is not divisible by 2. Dividing 12 again by 2, 12 ÷ 2 = 6. 6 is completely divisible by 2, hence, we again perform the division. Thus, 6 ÷ 2 = 3. For calculation, here's how to calculate Prime Factorization of 24 using the formula above, step by step instructions are given below 24 6 3 2 4 2 2 Cumulative all the circle value in multiply (times) format, like this: 2×2×2×3. You just get the Prime Factorization of that value (24). Frequently Asked QuestionsA factor tree can be used to determine the prime factors of 24, as shown in the figure. From the factor tree, we can see that the prime factorization of 24 is 2 × 2 × 2 × 3. This means 2 and 3 are the only prime factors of 24. Factor Pairs of 24. The factor pair of any number is a set of two integers that, when multiplied, result in that number.What are the factors of 24? Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. 3. How do you factor 24 on a calculator? All you have to do is provide the input value 24 and tap on the enter button next to the input field to obtain the factors. Here is the complete solution of finding Prime Factors of 24: The smallest Prime Number which can divide 24 without a remainder is 2. So the first calculation step would look like: 24 ÷ 2 = 12. Now we repeat this action until the result equals 1: 12 ÷ 2 = 6. 6 ÷ 2 = 3. 3 ÷ 3 = 1. A Factor Pair of number 24 is a combination of two factors which can be multiplied together to equal 24. List of all possible Factor Pairs of 24: 1 x 24 = 24 2 x 12 = 24 3 x 8 = 24 4 x 6 = 24 6 x 4 = 24 8 x 3 = 24 12 x 2 = 24 24 x 1 = 24 yamba caravan parkillinois tollwayAll Prime Factors of 24 : 2, 2, 2, 3 As we can see there is only one Prime Factor common to both numbers. It is 2 So 2 is the Greatest Common Factor of 10 and 24 Print Nearby homes similar to 24 Upperbend have recently sold between $1,475K to $1,740K at an average of $705 per square foot. SOLD APR 4, 2022. $1,530,000 Last Sold Price. 3 Beds. 3 Baths. 2,245 Sq. Ft. 29 Arrowhead, Irvine, CA 92618. SOLD MAY 24, 2022. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Now, to find the greatest common factor, we find the largest number that is on both lists. This number is 8. What's the GCF of 32 and 40? The GCF of 32 and 40 is 8.A Factor Pair of number 24 is a combination of two factors which can be multiplied together to equal 24. List of all possible Factor Pairs of 24: 1 x 24 = 24 2 x 12 = 24 3 x 8 = 24 4 x 6 = 24 6 x 4 = 24 8 x 3 = 24 12 x 2 = 24 24 x 1 = 24The factors of 24 can be defined as the numbers which are completely divisible by the number 24, or you can define it as two numbers when multiplied by each other, giving the result of 24. The factors of 24 can be listed as 1, 2, 3, 4, 6, 8, and 24. The factors of 24 have both a positive pair and a negative one. Sep 29, 2022 · Divide 24 with its smallest prime factor. Here, the smallest prime factor of 24 is 2. So, 24 ÷ 2 = 12. Repeated division of obtained quotient by 2 until we get a number that is not divisible by 2. Dividing 12 again by 2, 12 ÷ 2 = 6. 6 is completely divisible by 2, hence, we again perform the division. Thus, 6 ÷ 2 = 3. Important Points to Remember Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Prime factors of 24: 2 and 3 Pair factors of 24: (1, 24), (2, 12), (3, 8), and (4, 6). Prime factorisation of 24: 2 3 × 3 24 ÷ 12 = 2. 24 ÷ 24 = 1. The Postive Factors of 24 are therefore all the numbers we used to divide (divisors) above to get an even number. Here is the list of all Postive Factors of 24 in numerical order: 1, 2, 3, 4, 6, 8, 12, and 24. Factors of 24 include negative numbers. The factors of 24 are all of the factors of 24 that multiply together to equal twenty-four.Factors of 24 equal 1,2,3,4,6,8,12.24Prime factors of 24 equal 2,2...The partition was outlined in the Indian Independence Act 1947 and resulted in the dissolution of the British Raj, i.e., Crown rule in India. The two self-governing independent Dominions of India and Pakistan legally came into existence at midnight on 14–15 August 1947. The partition displaced between 10 and 20 million people along religious ... home depot bernalillo Sep 21, 2022 · The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and its negative factors are -1, -2, -3, -4, -6, -8, -12, -24. What is a prime factor of 24? Factors of 24 are basically the numbers that divide it evenly or exactly without leaving any remainder i.e if a number divides 24 with a remainder of zero, then that number is called a factor. How many common factors are there in 12, 24 and 36? A.4 B. 5 C.6 D.7. Answers: 2 Get Iba pang mga katanungan: Math. Math, 28.10.2019 16:29, girly61. 2.at the start of ... A factor is a number that goes into another number exactly. For example, 10 is a factor of 100 because 100 can be divided by 10. Factors of 24 refer to the numbers that can exactly divide 24 leaving the remainder 0.The best way to find the factors of any number is through division.Factors of Square Root of 24. Fraction Calculator. GCF of 16 and 24. GCF of 18 and 24. GCF of 24 and 30. GCF of 24 and 32. GCF of 24 and 36. GCF of 24 and 40. PEMDAS Calculator.Jul 24, 2007 · Results. Of 7100 cooks, 5835 (82%) replied to the questionnaire, including 1010 men and 4825 women. The mean age was 41.4 for men and 47.5 for women. What is the factors of 24? There are a total of eight factors of 24, they are 1, 2, 3, 4, 6, 8, 12 and 24. Pair factors of 24 are the numbers, which gives the 99 ford f 150 As we know factors of 24 are all the numbers that can exactly divide the number 24 simply divide 24 by all the numbers up to 24 to see the ones that result in zero remainders. Numbers that divide without remainder are factors and in this case below are the factors The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors. The number of prime factors of 24 is 2. Factor tree or prime decomposition for 24 As 24 is a composite number, we can draw its factor tree:The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors. The number of prime factors of 24 is 2. Factor tree or prime decomposition for 24 As 24 is a composite number, we can draw its factor tree:All Factors of 24 The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24! 24 has 8 factors in total. Factor Pairs of 24 Factor pairs are two whole numbers that multiply together to the original number. A factor pair of 24 is two numbers that multiply together to make 24. You should write factor pairs in brackets. The factor pairs of 24 are: (1, 24) Feb 08, 2010 · The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.The prime factors of 24 are: 2 and 3.The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40.The prime factors of 40 ... The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors. The number of prime factors of 24 is 2. Factor tree or prime decomposition for 24 As 24 is a composite number, we can draw its factor tree: 1 × 18 = 18 2 × 9 = 18 3 × 6 = 18 6 × 3 = 18 9 × 2 = 18 18 × 1 = 18 Like we said above, Factors of 18 include negative numbers. Minus times minus equals plus, thus you can convert the Positive Factor Pair list above by simply putting a minus in front of every factor to get all the Negative Factor Pairs of 18: -1 × -18 = 18 -2 × -9 = 18 -3 × -6 = 18The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Now, to find the greatest common factor, we find the largest number that is on both lists. This number is 8. What's the GCF of 32 and 40? The GCF of 32 and 40 is 8.Jan 30, 2018 · The factors of 24 that are composite numbers are 4, 6, 8, 12, and 24. What are all the composite numbers of 24? The composite factors of 24 are 2,4,6,8,12 and 24. Now let us know how to find the prime factors of a number. The first step is to divide the number 56 with the smallest prime factor, say 2. 56 ÷ 2 = 28 Again, divide 28 by 2 and the process goes on. 28 ÷ 2 = 14 14 ÷ 2 = 7 Now, if we divide 7 by 2 we will get a fractional number, which cannot be a factor.For calculation, here's how to calculate Prime Factorization of 24 using the formula above, step by step instructions are given below 24 6 3 2 4 2 2 Cumulative all the circle value in multiply (times) format, like this: 2×2×2×3. You just get the Prime Factorization of that value (24). Frequently Asked QuestionsFor calculation, here's how to calculate Prime Factorization of 24 using the formula above, step by step instructions are given below 24 6 3 2 4 2 2 Cumulative all the circle value in multiply (times) format, like this: 2×2×2×3. You just get the Prime Factorization of that value (24). Frequently Asked Questions🔢 Factors of 277. Find and list all factors of 277. Factors of 277 in Pairs. What is the Factors of 277? Answer: 1, 277. Factors of a Number - List all Factors and Factor Pairs of a Number chemist warehouse norwoodJul 19, 2022 · What are the factors of 24? Sol. 24 has a total of 8 factors and they are 1, 2, 3, 4, 6, 8, 12 and 24. Q. How to find the factors of a number? Sol. There are 2 ways of finding the factor of a number and these 1. Division Method 2. Prime Factorisation. Q. What are the factors of 24 in pairs? Sol. A Factor Pair of number 24 is a combination of two factors which can be multiplied together to equal 24. List of all possible Factor Pairs of 24: 1 x 24 = 24 2 x 12 = 24 3 x 8 = 24 4 x 6 = 24 6 x 4 = 24 8 x 3 = 24 12 x 2 = 24 24 x 1 = 24Step 1. Start dividing 24 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number. Step 2. After finding the smallest prime factor of the number 24, which is 2. Divide 24 by 2 to obtain the quotient (12). 24 ÷ 2 = 12. Step 3. Repeat step 1 with the obtained quotient (12).24 ÷ 2 = 12. 24 ÷ 2=12. This results in a whole number, so you can continue dividing by 2. 12 ÷ 2 = 6. 6 ÷ 2 = 3. 3 ÷ 2 = 1.5. This is not a whole number, so instead, try dividing by the next smallest prime factor 3. 3 ÷ 3 = 1. The result has reached 1, so all the prime factors needed to express 24 have been found. How many factors are there for 24? Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. So there are in total 8 factors. Raju wishes to write all the prime factors of 24. Can you assist him in doing the same? Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Prime factors of 24 are 2, 2, 2, 3.Factors of 242. Factors of 242 are 1, 2, 11, 22, 121. There are 5 integers that are factors of 242. The biggest factor of 242 is 121. Positive integers that divides 242 without a remainder are listed below. used audi r8Sep 21, 2022 · What is the factors of 24? There are a total of eight factors of 24, they are 1, 2, 3, 4, 6, 8, 12 and 24. Pair factors of 24 are the numbers, which gives the The number 24 has 8 factors and is a composite number. To calculate the factors of 24 we divide, whenever we can, among all the numbers that are less than it. 24:1=24 24:2=12 24:3=8 24:4=6 24:6=4 24:8=3 24:12=2 24:24=1. 0 Comments. Submit a Comment. Your email address will not be published. Required fields are marked * Comment * Name *The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors. The number of prime factors of 24 is 2. Factor tree or prime decomposition for 24 As 24 is a composite number, we can draw its factor tree:List of positive integer factors of 24 that divides 24 without a remainder. 1, 2, 3, 4, 6, 8, 12, 24 Greatest Common Factor We found the factors of 24 . The biggest common factor number is the GCF number. So the Greatest Common Factor 24 is 24. Therefore, GCF of numbers 24 is 24 Finding GCF of 24 using Prime Factorization Given Input Data is 24This calculator factors a set of positive integers to find the common factors (common divisors) of those integers. Enter the set of numbers you want to factor separating them with commas. Click "Calculate" to see all factors of each number as well as the greatest common factor (GCF). The factors of a number include all divisors of that number. A composite number is an integer that can be divided by at least another natural number, besides itself and 1, without leaving a remainder (divided exactly). The factorization or decomposition of 24 = 2 3 •3. Notice that here, it is written in exponential form. The prime factors of 24 are 2 and 3. It is the list of the integer's prime factors.Important Points to Remember Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Prime factors of 24: 2 and 3 Pair factors of 24: (1, 24), (2, 12), (3, 8), and (4, 6). Prime factorisation of 24: 2 3 × 3 Background. Low back pain (LBP) is the most frequently reported work-related disorder in Japan [].Various studies [2,3] have reported that among working populations, the rate of LBP due to heavy workload during the previous day [], week, month [5,6], or year [7-10], or during the lifetime [4,9,11] varies between 5.6% and 84.1% [].LBP is a common disorder among cooks working in school lunch ... penn state brandywine athletics xa