Greatest Common Factor of 972 and 975

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 972, 975 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 972 and 975 is 3.

GCF(972,975) = 3

GCF of 972 and 975

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

GCF of:
and

Greatest Common Factor of 972 and 975

GCF of 972 and 975 is 3

Prime Factorization of 972


2 972
2 486
3 243
3 81
3 27
3 9
3 3
1

Prime factors of 972 are 2,3. Prime factorization of 972 in exponential form is:

972 = 22×35

Prime Factorization of 975


3 975
5 325
5 65
13 13
1

Prime factors of 975 are 3,5,13. Prime factorization of 975 in exponential form is:

975 = 31×52×131

∴ So by taking common prime factors GCF of 972 and 975 is 3

Greatest Common Factor of 972 and 975 by matching factors method

Factors of 972

List of positive integer factors of 972 that divides 972 without a remainder.

1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972

Factors of 975

List of positive integer factors of 975 that divides 975 without a remainder.

1,3,5,13,15,25,39,65,75,195,325,975

Greatest Common Factor

We found the factors and prime factorization of 972 and 975. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 975 is 3.

Also check out the Least Common Multiple of 972 and 975

Properties of GCF 972 and 975

(i) The GCF of 972 and 975 is associative

GCF of 972 and 975 = GCF of 975 and 972

Related Greatest Common Factor of 972

Related Greatest Common Factor of 975

Frequently Asked Questions on GCF of 972 and 975

1. What is the GCF of 972 and 975?

Answer: GCF of 972 and 975 is 3.

2. What are the Factors of 972?

Answer: Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. There are 18 integers that are factors of 972. The greatest factor of 972 is 972.

3. What are the Factors of 975?

Answer: Factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975. There are 12 integers that are factors of 975. The greatest factor of 975 is 975.

4. How to Find the GCF of 972 and 975?

Answer:

Greatest Common Factor of 972 and 975 = 3

Step 1: Find the prime factorization of 972

972 = 2 x 2 x 3 x 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 975

975 = 3 x 5 x 5 x 13

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

GCF = 3

Step 4: Therefore, the greatest common factor of 972 and 975 is 3