Greatest Common Factor of 12 and 9

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 12, 9 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 12 and 9 is 3.

GCF(12,9) = 3

GCF of 12 and 9

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

GCF of:
and

Greatest Common Factor of 12 and 9

GCF of 12 and 9 is 3

Prime Factorization of 12


2 12
2 6
3 3
1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

Prime Factorization of 9


3 9
3 3
1

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 32

∴ So by taking common prime factors GCF of 12 and 9 is 3

Greatest Common Factor of 12 and 9 by matching factors method

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1,3,9

Greatest Common Factor

We found the factors and prime factorization of 12 and 9. The biggest common factor number is the GCF number.
So the greatest common factor 12 and 9 is 3.

Also check out the Least Common Multiple of 12 and 9

Properties of GCF 12 and 9

(i) The GCF of 12 and 9 is associative

GCF of 12 and 9 = GCF of 9 and 12

Related Greatest Common Factor of 12

Related Greatest Common Factor of 9

Frequently Asked Questions on GCF of 12 and 9

1. What is the GCF of 12 and 9?

Answer: GCF of 12 and 9 is 3.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

4. How to Find the GCF of 12 and 9?

Answer:

Greatest Common Factor of 12 and 9 = 3

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 9

9 = 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 12 and 9 is 3