# Greatest Common Divisor

Greatest Common Divisor (GCD) is the largest common factor of a number. It is also called as a greatest common factor (GCF).

## Finding the Greatest Common Divisor:

Say we have 3 numbers: 60, 132, and 96, and want to find the largest number that will divide evenly into each of these numbers. Two different methods can be used to find the solution to this problem.

#### Method I:

List the factors of each number and then identify the greatest number that is on every list.

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48. 96
So the greatest common factor would be 12

#### Method II:

Write the prime factorization of each number. The GCF is the product of the common prime factors. Notice that the prime number 2 occurs twice in each of the three numbers. So we have determined that the greatest common factor (GCF) is 2 • 2 • 3 = 12.

## GCF of terms that include variable:

In algebra, sometimes you need to find the greatest common factor with numbers that include variables. The strategies for finding the answers are very straightforward.

For example, consider finding the greatest common factor of 16x2y and 18xy2. First, find the prime factorization for both numbers as well as the factors of the variables:

16x2y = 2 • 2 • 2 • 2 • x • x • y

18xy2= 2 • 3 • 3 • x • y •y

Both the terms have 2, x and y in common. Therefore the GCD or GCF is 2xy.

12

17

79

360

198

2/3

3/5

20/54 = 10/27

0.9

2.7

2^2 x 3^5 x 7^2

12,24,36

27, 27×7

Total 4 pairs

Total 4 pairs

12×4, 12×3

111

## 18. The product of two numbers is 2028 and their HCF is 13. The number of such pairs is how many

Total pairs are 3