How many cards will be in each​ pile?

Question

Timmy has collected 150 football cards and 120 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

 

It is the greatest common factor (GCF) of 150 and 120

 

First prime factor 150:   150 = 15 x 10 = 5 x 3 x 5 x 2 = 2 x 3 x 5 x 5

Then prime factor 120:  120 = 12 x 10 = 2 x 2 x 3 x 2 x5 = 2 x 2 x 2 x 3 x 5

 

The prime factors they have in common is 2 x 3 x 5 = 30

So the greatest common factor is 30. It is the largest number

that divides into 120 and 150 evenly.

 

You can also find the GCF using Euclid's Method.

Just keep dividing by smaller remainder until the remainder is zero.

The last number you divided by is the GCF.

 

150/120 = 1 remainder 30.

120/30 = 4 remainder zero.

The last number we divided by to get a remainder of zero is 30.

 

So there will be 5 stacks of football cards and 4 stacks of baseball cards

with 30 cards in each stack.