I have a deck of 54 cards, and I deal all of the cards to x players, with each player getting y cards. If x is at least 2 and y is at least 5 , then how many possible values of x are there?
+23245 Since all the cards are dealt out, x must evenly divide into 54.
The numbers that are factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
So, when x = 1, y = 54; x = 2, y = 27; x = 3, y = 18; x = 6, y = 9; x = 9, y = 6; x = 18, y = 3; x = 27, y = 2; and x = 54, y = 1.
For x to be at least 2 and y to be at least 5, the possibilities are (2, 27), (3,18), (6,9), (9,6).
