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 cookies will there be in each pile?
To find the largest possible number of cookies in each pile, we need to find the greatest common divisor (GCD) of 300 and 264.
We can find the GCD using prime factorization:
300 = 2^2 * 3 * 5^2
264 = 2^3 * 3 * 11
The GCD is the product of the common prime factors, each raised to the smallest power they appear in both numbers:
GCD = 2^2 * 3 = 12
Therefore, there will be 12 cookies in each pile.