# What is the Greatest Common Factor of 10 and 14?

Greatest common factor (GCF) of 10 and 14 is **2**.

GCF(10,14) = 2

We will now calculate the prime factors of **10 and 14**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 10 and 14.

## How to find the GCF of 10 and 14?

We will first find the prime factorization of 10 and 14. After we will calculate the factors of 10 and 14 and find the biggest common factor number .

### Step-1: Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of **10** in exponential form is:

10 = 2^{1} × 5^{1}

### Step-2: Prime Factorization of 14

Prime factors of 14 are 2, 7. Prime factorization of **14** in exponential form is:

14 = 2^{1} × 7^{1}

### Step-3: Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5

### Step-4: Factors of 14

List of positive integer factors of 14 that divides 10 without a remainder.

1, 2, 7

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10 and 14. The biggest common factor number is the **GCF** number.

So the **greatest common factor 10 and 14** is **2**.

Also check out the Least Common Multiple of 10 and 14