Greatest Common Factor of 72 and 90

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 72, 90 i.e. 18 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 72 and 90 is 18.

GCF(72,90) = 18

GCF of 72 and 90

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

GCF of:
and

Greatest Common Factor of 72 and 90

GCF of 72 and 90 is 18

Prime Factorization of 72


2 72
2 36
2 18
3 9
3 3
1

Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:

72 = 23×32

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

∴ So by taking common prime factors GCF of 72 and 90 is 18

Greatest Common Factor of 72 and 90 by matching factors method

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

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

Greatest Common Factor

We found the factors and prime factorization of 72 and 90. The biggest common factor number is the GCF number.
So the greatest common factor 72 and 90 is 18.

Also check out the Least Common Multiple of 72 and 90

Properties of GCF 72 and 90

(i) The GCF of 72 and 90 is associative

GCF of 72 and 90 = GCF of 90 and 72

Related Greatest Common Factor of 72

Related Greatest Common Factor of 90

Frequently Asked Questions on GCF of 72 and 90

1. What is the GCF of 72 and 90?

Answer: GCF of 72 and 90 is 18.

2. What are the Factors of 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

3. 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.

4. How to Find the GCF of 72 and 90?

Answer:

Greatest Common Factor of 72 and 90 = 18

Step 1: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 90

90 = 2 x 3 x 3 x 5

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 72 and 90 is 18