# What is the Greatest Common Factor of 6 and 21?

Greatest common factor (GCF) of 6 and 21 is **3**.

GCF(6,21) = 3

We will now calculate the prime factors of **6 and 21**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 6 and 21.

## How to find the GCF of 6 and 21?

We will first find the prime factorization of 6 and 21. After we will calculate the factors of 6 and 21 and find the biggest common factor number .

### Step-1: Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of **6** in exponential form is:

6 = 2^{1} × 3^{1}

### Step-2: Prime Factorization of 21

Prime factors of 21 are 3, 7. Prime factorization of **21** in exponential form is:

21 = 3^{1} × 7^{1}

### Step-3: Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3

### Step-4: Factors of 21

List of positive integer factors of 21 that divides 6 without a remainder.

1, 3, 7

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6 and 21. The biggest common factor number is the **GCF** number.

So the **greatest common factor 6 and 21** is **3**.

Also check out the Least Common Multiple of 6 and 21