# What is the Greatest Common Factor of 10 and 12?

Greatest common factor (GCF) of 10 and 12 is **2**.

GCF(10,12) = 2

We will now calculate the prime factors of **10 and 12**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 10 and 12.

## How to find the GCF of 10 and 12?

We will first find the prime factorization of 10 and 12. After we will calculate the factors of 10 and 12 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 12

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

12 = 2^{2} × 3^{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 12

List of positive integer factors of 12 that divides 10 without a remainder.

1, 2, 3, 4, 6

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10 and 12. The biggest common factor number is the **GCF** number.

So the **greatest common factor 10 and 12** is **2**.

Also check out the Least Common Multiple of 10 and 12