Greatest Common Factor of 9 and 21

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 9, 21 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 9 and 21 is 3.

GCF(9,21) = 3

GCF of 9 and 21

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

GCF of:
and

Greatest Common Factor of 9 and 21

GCF of 9 and 21 is 3

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

Prime Factorization of 21


3 21
7 7
1

Prime factors of 21 are 3.Prime factorization of 21 in exponential form is:

21 = 31×71

∴ So by taking common prime factors GCF of 9 and 21 is 3

Greatest Common Factor of 9 and 21 by matching factors method

Factors of 9

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

1,3,9

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Greatest Common Factor

We found the factors and prime factorization of 9 and 21. The biggest common factor number is the GCF number.
So the greatest common factor 9 and 21 is 3.

Also check out the Least Common Multiple of 9 and 21

Properties of GCF 9 and 21

(i) The GCF of 9 and 21 is associative

GCF of 9 and 21 = GCF of 21 and 9

Related Greatest Common Factor of 9

Related Greatest Common Factor of 21

Frequently Asked Questions on GCF of 9 and 21

1. What is the GCF of 9 and 21?

Answer: GCF of 9 and 21 is 3.

2. 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.

3. What are the Factors of 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the GCF of 9 and 21?

Answer:

Greatest Common Factor of 9 and 21 = 3

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 21

21 = 3 x 7

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 9 and 21 is 3