Greatest Common Factor of 969 and 972

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 969, 972 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 969 and 972 is 3.

GCF(969,972) = 3

GCF of 969 and 972

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

GCF of:
and

Greatest Common Factor of 969 and 972

GCF of 969 and 972 is 3

Prime Factorization of 969


3 969
17 323
19 19
1

Prime factors of 969 are 3,17,19. Prime factorization of 969 in exponential form is:

969 = 31×171×191

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

∴ So by taking common prime factors GCF of 969 and 972 is 3

Greatest Common Factor of 969 and 972 by matching factors method

Factors of 969

List of positive integer factors of 969 that divides 969 without a remainder.

1,3,17,19,51,57,323,969

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

Greatest Common Factor

We found the factors and prime factorization of 969 and 972. The biggest common factor number is the GCF number.
So the greatest common factor 969 and 972 is 3.

Also check out the Least Common Multiple of 969 and 972

Properties of GCF 969 and 972

(i) The GCF of 969 and 972 is associative

GCF of 969 and 972 = GCF of 972 and 969

Related Greatest Common Factor of 969

Related Greatest Common Factor of 972

Frequently Asked Questions on GCF of 969 and 972

1. What is the GCF of 969 and 972?

Answer: GCF of 969 and 972 is 3.

2. What are the Factors of 969?

Answer: Factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969. There are 8 integers that are factors of 969. The greatest factor of 969 is 969.

3. 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.

4. How to Find the GCF of 969 and 972?

Answer:

Greatest Common Factor of 969 and 972 = 3

Step 1: Find the prime factorization of 969

969 = 3 x 17 x 19

Step 2: Find the prime factorization of 972

972 = 2 x 2 x 3 x 3 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 = 3

Step 4: Therefore, the greatest common factor of 969 and 972 is 3