Question

Kobe has collected 300 football cards and 264 baseball cards. He wants to divide them into piles so that each pile has only one type of card, there is the same number of cards in each pile, and each pile has the greatest possible number of cards. How many cards will be in each pile?

Answer 1

To divide 300 football cards and 264 baseball cards into the largest equal-sized piles, find the greatest common divisor (GCD), which is 12. Thus, there will be 12 cards in each pile.

Step-by-step explanation:

The question asks how to divide 300 football cards and 264 baseball cards into piles where each pile only contains one type of card, has an equal number of cards, and each pile has the greatest possible number of cards.

1. Determine the total number of each type of card: 300 football cards and 264 baseball cards.
2. Find the greatest common divisor (GCD) for the numbers 300 and 264 to determine the largest stack size that can be the same for both types of cards.
3. The GCD of 300 and 264 is 12. This can be found using the Euclidean algorithm or by listing the factors of both numbers and finding the largest common factor.
4. Once the GCD is found, divide the total number of football cards by 12 (300/12) to get 25 piles of football cards.
5. Similarly, divide the total number of baseball cards by 12 (264/12) to get 22 piles of baseball cards.

There will be 12 cards in each pile, with 25 piles for football cards and 22 piles for baseball cards.