# What is the Greatest Common Factor of 12 and 26?

Greatest common factor (GCF) of 12 and 26 is **2**.

GCF(12,26) = 2

We will now calculate the prime factors of **12 and 26**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 12 and 26.

## How to find the GCF of 12 and 26?

We will first find the prime factorization of 12 and 26. After we will calculate the factors of 12 and 26 and find the biggest common factor number .

### Step-1: 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-2: Prime Factorization of 26

Prime factors of 26 are 2, 13. Prime factorization of **26** in exponential form is:

26 = 2^{1} × 13^{1}

### Step-3: Factors of 12

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

1, 2, 3, 4, 6

### Step-4: Factors of 26

List of positive integer factors of 26 that divides 12 without a remainder.

1, 2, 13

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12 and 26. The biggest common factor number is the **GCF** number.

So the **greatest common factor 12 and 26** is **2**.

Also check out the Least Common Multiple of 12 and 26