# What is the Greatest Common Factor of 21 and 37?

Greatest common factor (GCF) of 21 and 37 is **1**.

GCF(21,37) = 1

We will now calculate the prime factors of **21 and 37**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 21 and 37.

## How to find the GCF of 21 and 37?

We will first find the prime factorization of 21 and 37. After we will calculate the factors of 21 and 37 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 37

Prime factors of 37 are 37. Prime factorization of **37** in exponential form is:

37 = 37^{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 37

List of positive integer factors of 37 that divides 21 without a remainder.

1

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21 and 37. The biggest common factor number is the **GCF** number.

So the **greatest common factor 21 and 37** is **1**.

Also check out the Least Common Multiple of 21 and 37