AN EASIER WAY to find the GCF

An EASIER WAY to find the GCF (Greatest Common Factor)

The two traditional methods taught to find the GCF are:

1. Prime Factorization

2. Determining, separately, the factors for BOTH numbers, to find the largest number appearing in both lists.

Gary Pearlson’s easier, better method:

1. Determine JUST the factors of the smaller number (by creating a two sided “factor tree”.)

2. During each “tree” step in part 1, test the right side number to see if it is also a factor of the larger number.

The first right side tree number that’s also a factor of the larger number is the GCF.

3. If no right side number is the GCF (example 2), continue testing using the tree’s left side numbers, moving upwards.

Example 1: What is the GCF of 30 and 45??

30 45

1 30 Is 30 a factor of 45? Answer: No (so continue creating the factor tree.)

30 45

1 30

2 15 Is 15 a factor of 45? Answer: YES and thus 15 is the GCF of 30 and 45.

Example 2: What is the GCF of 30 and 51??

30 51

Factor of 51?

1 30 No

2 15 No

3 10 No When the factor tree completes

5 6 No without any right side number being

the GCF, continue testing up the left side.

30 51

1 30

2 15

33 10 Is 3 a factor of 51? Answer: YES and thus 3 is the GCF of 30 and 51.

5 6