Example: Find the GCF of 24 and 18.

You can get the GCF of 24 and 18 by using the listing method.

Step 1. List all factors of 24 and 18.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 18: 1, 2, 3, 6, 9, 18

Step 2. Identify the common factors of 24 and 18.

Common factors: 1, 2, 3, 6

Step 3. Get the greatest number in the set of common factors.

GCF of 24 and 18 is 6.

Example: Find the GCF of 36 and 45.

List all factors of 36 and 45.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 45: 1, 3, 5, 9, 15, 45

Common factors: 1, 3, 9

Thus, the GCF of 36 and 45 is 9.

Aside from listing the factors, another way of finding the GCF of two numbers is through prime factorization.

If the numbers have 1 as their GCF, they are said to be relatively prime numbers.

Factors of 8: 1, 2, 4, 8

Factors of 15: 1, 3, 5, 15

The only common factor of 8 and 15 is 1, hence 8 and 15 are relatively prime numbers. The GCF of relatively prime numbers is 1.

You can also get the GCF of two numbers using the Euclidean algorithm.

Study the example to understand the procedure.

Example: Use Euclidean algorithm to fi nd the GCF of 12 and 40.

Solution: Follow the indicated steps to fi nd the GCF of 12 and 40.

Example: Use Euclidean algorithm to fi nd the GCF of 24 and 8.

Solution: First, divide the greater number by the lesser number:

24 ÷ 8 = 3 R 0.

Since division is exact, then the GCF of 24 and 8 is the last divisor, which is also the lesser number. Hence, the GCF of 24 and 8 is 8.

If, in a pair of numbers, the lesser one can exactly divide the greater number, the GCF of the pair is the lesser number.