Question

a deck of cards has 52 cards. the deck can be divided into 4 piles of exactly 13 cards each. describe all the other ways that can be divided into equal piles.

Answer 1

Since 7^2=49 and 8^2=64, any factors found after 7 would be redundant. Trying out 1, we can get 52/1=52, which means 52 stacks of 1 or 1 stack of 52. For 2, we get 52/2=26, so 2 stacks of 26 or 26 stacks of 2. 3 doesn't work, and we could get 13 piles of 4 as 13*4=52. Next, 5 doesn't work, as well as 6 and 7, so we're done