# Greatest Common Factor of 16 and 21

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 16, 21 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 16 and 21 is 1.

GCF(16,21) = 1

## GCF of 16 and 21

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

GCF of:
and

### Greatest Common Factor of 16 and 21 by Prime factorization method

Prime Factorization of 16

 2 16 2 8 2 4 2 2 1

Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:

16 = 24

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 16 and 21 is 1

### Greatest Common Factor of 16 and 21 by matching factors method

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

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 16 and 21. The biggest common factor number is the GCF number.
So the greatest common factor 16 and 21 is 1.

Also check out the Least Common Multiple of 16 and 21

### Properties of GCF 16 and 21

(i) The GCF of 16 and 21 is associative

GCF of 16 and 21 = GCF of 21 and 16

### Frequently Asked Questions on GCF of 16 and 21

1. What is the GCF of 16 and 21?

Answer: GCF of 16 and 21 is 1.

2. What are the Factors of 16?

Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.

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 16 and 21?

Greatest Common Factor of 16 and 21 = 1

Step 1: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

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 = = 1

Step 4: Therefore, the greatest common factor of 16 and 21 is 1