Greatest Common Factor of 972 and 974

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, 974 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 972 and 974 is 2.

GCF(972,974) = 2

GCF of 972 and 974

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

GCF of:
and

Greatest Common Factor of 972 and 974

GCF of 972 and 974 is 2

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 974


2 974
487 487
1

Prime factors of 974 are 2,487. Prime factorization of 974 in exponential form is:

974 = 21×4871

∴ So by taking common prime factors GCF of 972 and 974 is 2

Greatest Common Factor of 972 and 974 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 974

List of positive integer factors of 974 that divides 974 without a remainder.

1,2,487,974

Greatest Common Factor

We found the factors and prime factorization of 972 and 974. The biggest common factor number is the GCF number.
So the greatest common factor 972 and 974 is 2.

Also check out the Least Common Multiple of 972 and 974

Properties of GCF 972 and 974

(i) The GCF of 972 and 974 is associative

GCF of 972 and 974 = GCF of 974 and 972

Related Greatest Common Factor of 972

Related Greatest Common Factor of 974

Frequently Asked Questions on GCF of 972 and 974

1. What is the GCF of 972 and 974?

Answer: GCF of 972 and 974 is 2.

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 974?

Answer: Factors of 974 are 1, 2, 487, 974. There are 4 integers that are factors of 974. The greatest factor of 974 is 974.

4. How to Find the GCF of 972 and 974?

Answer:

Greatest Common Factor of 972 and 974 = 2

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 974

974 = 2 x 487

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

GCF = 2

Step 4: Therefore, the greatest common factor of 972 and 974 is 2