Greatest Common Factor of 21 and 30

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

Greatest common factor (GCF) of 21 and 30 is 3.

GCF(21,30) = 3

GCF of 21 and 30

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

GCF of:
and

Greatest Common Factor of 21 and 30

GCF of 21 and 30 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 30


2 30
3 15
5 5
1

Prime factors of 30 are 2,3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

∴ So by taking common prime factors GCF of 21 and 30 is 3

Greatest Common Factor of 21 and 30 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 30

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

Greatest Common Factor

We found the factors and prime factorization of 21 and 30. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 30 is 3.

Also check out the Least Common Multiple of 21 and 30

Properties of GCF 21 and 30

(i) The GCF of 21 and 30 is associative

GCF of 21 and 30 = GCF of 30 and 21

Related Greatest Common Factor of 21

Related Greatest Common Factor of 30

Frequently Asked Questions on GCF of 21 and 30

1. What is the GCF of 21 and 30?

Answer: GCF of 21 and 30 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 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

4. How to Find the GCF of 21 and 30?

Answer:

Greatest Common Factor of 21 and 30 = 3

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 30

30 = 2 x 3 x 5

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 30 is 3