# What is the Greatest Common Factor of 34 and 42?

Greatest common factor (GCF) of 34 and 42 is **2**.

GCF(34,42) = 2

We will now calculate the prime factors of **34 and 42**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 34 and 42.

## How to find the GCF of 34 and 42?

We will first find the prime factorization of 34 and 42. After we will calculate the factors of 34 and 42 and find the biggest common factor number .

### Step-1: Prime Factorization of 34

Prime factors of 34 are 2, 17. Prime factorization of **34** in exponential form is:

34 = 2^{1} × 17^{1}

### Step-2: 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-3: Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1, 2, 17

### Step-4: Factors of 42

List of positive integer factors of 42 that divides 34 without a remainder.

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

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34 and 42. The biggest common factor number is the **GCF** number.

So the **greatest common factor 34 and 42** is **2**.

Also check out the Least Common Multiple of 34 and 42