Greatest Common Factor of 90 and 108

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 90, 108 i.e. 18 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 90 and 108 is 18.

GCF(90,108) = 18

GCF of 90 and 108

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 90 and 108

GCF of 90 and 108 is 18

Prime Factorization of 90


2 90
3 45
3 15
5 5
1

Prime factors of 90 are 2,3,5. Prime factorization of 90 in exponential form is:

90 = 21×32×51

Prime Factorization of 108


2 108
2 54
3 27
3 9
3 3
1

Prime factors of 108 are 2,3. Prime factorization of 108 in exponential form is:

108 = 22×33

∴ So by taking common prime factors GCF of 90 and 108 is 18

Greatest Common Factor of 90 and 108 by matching factors method

Factors of 90

List of positive integer factors of 90 that divides 90 without a remainder.

1,2,3,5,6,9,10,15,18,30,45,90

Factors of 108

List of positive integer factors of 108 that divides 108 without a remainder.

1,2,3,4,6,9,12,18,27,36,54,108

Greatest Common Factor

We found the factors and prime factorization of 90 and 108. The biggest common factor number is the GCF number.
So the greatest common factor 90 and 108 is 18.

Also check out the Least Common Multiple of 90 and 108

Properties of GCF 90 and 108

(i) The GCF of 90 and 108 is associative

GCF of 90 and 108 = GCF of 108 and 90

Related Greatest Common Factor of 90

Related Greatest Common Factor of 108

Frequently Asked Questions on GCF of 90 and 108

1. What is the GCF of 90 and 108?

Answer: GCF of 90 and 108 is 18.

2. What are the Factors of 90?

Answer: Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. There are 12 integers that are factors of 90. The greatest factor of 90 is 90.

3. What are the Factors of 108?

Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.

4. How to Find the GCF of 90 and 108?

Answer:

Greatest Common Factor of 90 and 108 = 18

Step 1: Find the prime factorization of 90

90 = 2 x 3 x 3 x 5

Step 2: Find the prime factorization of 108

108 = 2 x 2 x 3 x 3 x 3

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 x 3 = 18

Step 4: Therefore, the greatest common factor of 90 and 108 is 18