# Greatest Common Factor of 21 and 28

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 21, 28 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 21 and 28 is 7.

GCF(21,28) = 7

## GCF of 21 and 28

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

GCF of:
and

### Greatest Common Factor of 21 and 28 by Prime factorization method

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 28

 2 28 2 14 7 7 1

Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:

28 = 22×71

∴ So by taking common prime factors GCF of 21 and 28 is 7

### Greatest Common Factor of 21 and 28 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 28

List of positive integer factors of 28 that divides 28 without a remainder.

1,2,4,7,14,28

Greatest Common Factor

We found the factors and prime factorization of 21 and 28. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 28 is 7.

Also check out the Least Common Multiple of 21 and 28

### Properties of GCF 21 and 28

(i) The GCF of 21 and 28 is associative

GCF of 21 and 28 = GCF of 28 and 21

### Frequently Asked Questions on GCF of 21 and 28

1. What is the GCF of 21 and 28?

Answer: GCF of 21 and 28 is 7.

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 28?

Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.

4. How to Find the GCF of 21 and 28?

Greatest Common Factor of 21 and 28 = 7

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 28

28 = 2 x 2 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 21 and 28 is 7