Greatest Common Factor of 18 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 18, 21 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 18 and 21 is 3.

GCF(18,21) = 3

GCF of 18 and 21

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

GCF of:
and

Greatest Common Factor of 18 and 21

GCF of 18 and 21 is 3

Prime Factorization of 18


2 18
3 9
3 3
1

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 21×32

Prime Factorization of 21


3 21
7 7
1

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 31×71

∴ So by taking common prime factors GCF of 18 and 21 is 3

Greatest Common Factor of 18 and 21 by matching factors method

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1,2,3,6,9,18

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 18 and 21. The biggest common factor number is the GCF number.
So the greatest common factor 18 and 21 is 3.

Also check out the Least Common Multiple of 18 and 21

Properties of GCF 18 and 21

(i) The GCF of 18 and 21 is associative

GCF of 18 and 21 = GCF of 21 and 18

Related Greatest Common Factor of 18

Related Greatest Common Factor of 21

Frequently Asked Questions on GCF of 18 and 21

1. What is the GCF of 18 and 21?

Answer: GCF of 18 and 21 is 3.

2. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

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 18 and 21?

Answer:

Greatest Common Factor of 18 and 21 = 3

Step 1: Find the prime factorization of 18

18 = 2 x 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 18 and 21 is 3