# What is the GCF of 6 and 21?

Greatest Common Factor of 6 and 21 is the greatest possible number which divides both 6 and 21 exactly.

## Answer: GCF of 6 and 21 is 3

Here, we will show two methods to find the GCF (6, 21)

## Explanation:

The methods to find GCF of 6 and 21 are

- GCF of 6 and 21 by Prime Factorisation Method
- GCF of 6 and 21 by Long Division

### Method 1: GCF of 6 and 21 by Prime Factorisation Method

Prime Factorisation of 6: ** **2 × 3

Prime Factorisation of 21: ** **3 × 7** **

Common Factors of 6 and 21: 3

Hence the greatest common factor of 6 and 21 is 3, that is, GCF of 6 and 21 is 3.

### Method 2: GCF of 6 and 21 by Long Division

- Divide 21 by 6 and check the remainder. Here, the remainder is 3
- The remainder 3 becomes the new divisor and the divisor 6 becomes the new dividend now. Follow the same step.
- Continue till you get the remainder as 0 and GCF of 6 and 21 will be the last divisor of this process.

So, GCF of 6 and 21 is 3

You can find the GCF of 6 and 21 in any of the above methods but the solution will be the same.