# Greatest Common Factor of 21 and 27

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 21, 27 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 21 and 27 is 3.

GCF(21,27) = 3

## GCF of 21 and 27

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

GCF of:
and

### Greatest Common Factor of 21 and 27 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 27

 3 27 3 9 3 3 1

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 33

∴ So by taking common prime factors GCF of 21 and 27 is 3

### Greatest Common Factor of 21 and 27 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 27

List of positive integer factors of 27 that divides 27 without a remainder.

1,3,9,27

Greatest Common Factor

We found the factors and prime factorization of 21 and 27. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 27 is 3.

Also check out the Least Common Multiple of 21 and 27

### Properties of GCF 21 and 27

(i) The GCF of 21 and 27 is associative

GCF of 21 and 27 = GCF of 27 and 21

### Frequently Asked Questions on GCF of 21 and 27

1. What is the GCF of 21 and 27?

Answer: GCF of 21 and 27 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 27?

Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.

4. How to Find the GCF of 21 and 27?

Greatest Common Factor of 21 and 27 = 3

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 27

27 = 3 x 3 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 27 is 3