Greatest Common Factor of 21 and 24

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 21, 24 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 21 and 24 is 3.

GCF(21,24) = 3

GCF of 21 and 24

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

GCF of:
and

Greatest Common Factor of 21 and 24

GCF of 21 and 24 is 3

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

Prime Factorization of 24


2 24
2 12
2 6
3 3
1

Prime factors of 24 are 2,3. Prime factorization of 24 in exponential form is:

24 = 23×31

∴ So by taking common prime factors GCF of 21 and 24 is 3

Greatest Common Factor of 21 and 24 by matching factors method

Factors of 21

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

1,3,7,21

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

1,2,3,4,6,8,12,24

Greatest Common Factor

We found the factors and prime factorization of 21 and 24. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 24 is 3.

Also check out the Least Common Multiple of 21 and 24

Properties of GCF 21 and 24

(i) The GCF of 21 and 24 is associative

GCF of 21 and 24 = GCF of 24 and 21

Related Greatest Common Factor of 21

Related Greatest Common Factor of 24

Frequently Asked Questions on GCF of 21 and 24

1. What is the GCF of 21 and 24?

Answer: GCF of 21 and 24 is 3.

2. 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.

3. What are the Factors of 24?

Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are 8 integers that are factors of 24. The greatest factor of 24 is 24.

4. How to Find the GCF of 21 and 24?

Answer:

Greatest Common Factor of 21 and 24 = 3

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 24

24 = 2 x 2 x 2 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 21 and 24 is 3