# What is the Greatest Common Factor of 21 and 31?

Greatest common factor (GCF) of 21 and 31 is **1**.

GCF(21,31) = 1

We will now calculate the prime factors of **21 and 31**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 21 and 31.

## How to find the GCF of 21 and 31?

We will first find the prime factorization of 21 and 31. After we will calculate the factors of 21 and 31 and find the biggest common factor number .

### Step-1: 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-2: Prime Factorization of 31

Prime factors of 31 are 31. Prime factorization of **31** in exponential form is:

31 = 31^{1}

### Step-3: Factors of 21

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

1, 3, 7

### Step-4: Factors of 31

List of positive integer factors of 31 that divides 21 without a remainder.

1

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21 and 31. The biggest common factor number is the **GCF** number.

So the **greatest common factor 21 and 31** is **1**.

Also check out the Least Common Multiple of 21 and 31