# What is the Greatest Common Factor of 42 and 52?

Greatest common factor (GCF) of 42 and 52 is **2**.

GCF(42,52) = 2

We will now calculate the prime factors of **42 and 52**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 42 and 52.

## How to find the GCF of 42 and 52?

We will first find the prime factorization of 42 and 52. After we will calculate the factors of 42 and 52 and find the biggest common factor number .

### Step-1: Prime Factorization of 42

Prime factors of 42 are 2, 3, 7. Prime factorization of **42** in exponential form is:

42 = 2^{1} × 3^{1} × 7^{1}

### Step-2: Prime Factorization of 52

Prime factors of 52 are 2, 13. Prime factorization of **52** in exponential form is:

52 = 2^{2} × 13^{1}

### Step-3: Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21

### Step-4: Factors of 52

List of positive integer factors of 52 that divides 42 without a remainder.

1, 2, 4, 13, 26

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42 and 52. The biggest common factor number is the **GCF** number.

So the **greatest common factor 42 and 52** is **2**.

Also check out the Least Common Multiple of 42 and 52