A bakery has 300 chocolate chip cookies and 264 peanut butter cookies. The bakers wish to divide the chocolate chip cookies into piles and the peanut butter cookies into piles so that each pile has only one type of cookie, there is the same number of cookies in each pile, and each pile has the largest possible number of cookies.
How many piles of chocolate chip cookies will there be?
How many piles of peanut butter cookies will there be?
In order to divide the chocolate chip cookies into equal piles, we need to find the greatest common factor (GCF) of 300.
The prime factorization of 300 is 2^2 * 3 * 5^2.
To find the GCF, we take the highest exponent of each prime factor that appears in the prime factorization of 300. In this case, it is 2^2 * 3 * 5. Therefore, the GCF is 2^2 * 3 * 5 = 60.
So, there will be 60 piles of chocolate chip cookies.
We use the same process to find the number of piles of peanut butter cookies.
The prime factorization of 264 is 2^3 * 3 * 11.
The GCF is 2^3 * 3 = 24.
Therefore, there will be 24 piles of peanut butter cookies.