Greatest Common Factor of 7 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 7, 21 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 7 and 21 is 7.

GCF(7,21) = 7

GCF of 7 and 21

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

GCF of:
and

Greatest Common Factor of 7 and 21

GCF of 7 and 21 is 7

Prime Factorization of 7


7 7
1

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

7 = 71

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 7 and 21 is 7

Greatest Common Factor of 7 and 21 by matching factors method

Factors of 7

List of positive integer factors of 7 that divides 7 without a remainder.

1,7

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 7 and 21. The biggest common factor number is the GCF number.
So the greatest common factor 7 and 21 is 7.

Also check out the Least Common Multiple of 7 and 21

Properties of GCF 7 and 21

(i) The GCF of 7 and 21 is associative

GCF of 7 and 21 = GCF of 21 and 7

Related Greatest Common Factor of 7

Related Greatest Common Factor of 21

Frequently Asked Questions on GCF of 7 and 21

1. What is the GCF of 7 and 21?

Answer: GCF of 7 and 21 is 7.

2. What are the Factors of 7?

Answer: Factors of 7 are 1, 7. There are 2 integers that are factors of 7. The greatest factor of 7 is 7.

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 7 and 21?

Answer:

Greatest Common Factor of 7 and 21 = 7

Step 1: Find the prime factorization of 7

7 = 7

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 = 7

Step 4: Therefore, the greatest common factor of 7 and 21 is 7