# What is the Greatest Common Factor of 12 and 21?

Greatest common factor (GCF) of 12 and 21 is **3**.

GCF(12,21) = 3

We will now calculate the prime factors of **12 and 21**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 12 and 21.

## How to find the GCF of 12 and 21?

We will first find the prime factorization of 12 and 21. After we will calculate the factors of 12 and 21 and find the biggest common factor number .

### Step-1: Prime Factorization of 12

Prime factors of 12 are 2, 3. Prime factorization of **12** in exponential form is:

12 = 2^{2} × 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 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6

### Step-4: Factors of 21

List of positive integer factors of 21 that divides 12 without a remainder.

1, 3, 7

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12 and 21. The biggest common factor number is the **GCF** number.

So the **greatest common factor 12 and 21** is **3**.

Also check out the Least Common Multiple of 12 and 21