# What is the Greatest Common Factor of 15 and 21?

Greatest common factor (GCF) of 15 and 21 is **3**.

GCF(15,21) = 3

We will now calculate the prime factors of **15 and 21**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 15 and 21.

## How to find the GCF of 15 and 21?

We will first find the prime factorization of 15 and 21. After we will calculate the factors of 15 and 21 and find the biggest common factor number .

### Step-1: Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of **15** in exponential form is:

15 = 3^{1} × 5^{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 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5

### Step-4: Factors of 21

List of positive integer factors of 21 that divides 15 without a remainder.

1, 3, 7

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15 and 21. The biggest common factor number is the **GCF** number.

So the **greatest common factor 15 and 21** is **3**.

Also check out the Least Common Multiple of 15 and 21