EDGE Math 8

Factoring Numbers

Example

Express each of the numbers 12, 16, 18, 36, 49, and 54 as a product of prime numbers.

Solution

12 = 2^{2} \cdot 3

18 = 2 \cdot 3^{2}

49 = 7^{2}

16 = 2^{4}

36 = 2^{2} \cdot 3^{2}

54 = 2 \cdot 3^{3}

Consider the factors of 36 and 54.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Observe that the common factors of 36 and 54 are 1, 2, 3, 6, 9, and 18. The greatest among these factors is 18. You call 18 the greatest common factor (GCF) of 36 and 54.

Example

Find the GCF of each set of numbers.

{4, 8}

{45, 75}

{42, 96, 120}

Solution

1. 4

2. 15

3. 6