Directions:Read,analyze and solve the situation using prime factorization.

1. Juan has 72 cups and 64 glasses.If he will put it on the tray with same number of cups and glass,what is the biggest possible number of cups and glasses that the tray will contain?

72 64

GCF: ___________________

The biggest possible number of cups and glasses that the tray will contain is 8. To solve for this, we need to find for the Greatest Common Factor of 72 and 64. We will factor both 72 and 64 using either the listing method or the tree method.

Solutions:

List all the factors of 72.

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

List all the factors of 64.

64 - 1, 2, 4, 8, 16, 32, and 64

From the lists above, choose all the common factors between 72 and 64.

72 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 7264 - 1, 2, 4, 8, 16, 32, and 64

__________________________________

Common Factors: 1, 2, 4, and 8

Choose the greatest among the common factors of 72 and 64.

Common Factors: 1, 2, 4, and 8

Greatest: 8

Since, the Greatest Common Factor of 72 and 64 is 8.

Therefore, the biggest possible number of cups and glasses that the tray will contain is 8.

Keywords: Greatest Common Factor, factors

How to find for the Greatest Common Factor of two numbers: