Question

If you and your friend had a bunch of coins and wanted to put them in equal piles. You have 96 coins

and your friend has 72 coins. If you were to both make equal piles with no coins left over, what are
the different pile sizes?

Answer 1

9514 1404 393

Answer:

you both can make piles of 1, 2, 3, 4, 6, 8, 12, or 24 coins

Explanation:

Divisors of 96 are ...

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Divisors of 72 are ...

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

You can make equal piles of any of the number of coins that are divisors of 96, 2 piles of 48 or 48 piles of 2, for example.

Your friend can make equal piles of any of the number that are divisors of 72, 2 piles of 36, or 36 piles of 2, for example.

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If you both want to make piles of the same height, you both can make piles using any of the common divisors: 1, 2, 3, 4, 6, 8, 12, 24. (These are divisors of the greatest common divisor, 24.)