# What is the GCF of 68 and 102?

GCF (Greatest Common Factor) of two numbers is the largest possible number which divides the two numbers exactly without leaving any remainder.

## Answer: GCF of 68 and 102 is 34

We will explain two methods to find the GCF of 68 and 102

## Explanation:

The two methods that we are using to find GCF of 68 and 102 are shown below.

- GCF of 68 and 102 by Listing the Common Factors
- GCF of 68 and 102 by Prime Factorization

### Method 1: GCF of 68 and 102 by Listing the Common Factors

The factors of 68 and 102 are shown below

The common factors of 68 and 102 are 1, 2, 17, and 34.

Clearly, the greatest common factor is 34.

So, GCF of 68 and 102 is 34.

### Method 2: GCF of 68 and 102 by Prime Factorization

We will represent 68 and 102 as a product of their prime factors.

Prime factorization of 68 is 2 × 2 × 17

Prime factorization of 102 is 2 × 3 × 17

Common prime factors are 2 and 17.

GCF is the product of the factors that are common to each of the given numbers.

GCF of 68 and 102 is 2 × 17 = 34

Irrespective of the method, the solution to our question GCF of 68 and 102 is the same.