# What is the GCF of 34 and 85

GCF (Greatest Common Factor) of 34 and 85 is the largest possible number which divides 34 and 85 exactly without any remainder.

## Answer: GCF of 34 and 85 is 17

Two methods to find the GCF of 34 and 85 are explained below.

## Explanation:

The greatest common factor of 34 and 85 is the greatest number which divides the numbers 34 and 85 exactly. We will use the two methods to find the GCF of 34 and 85.

- Prime factorization Method
- Listing the common factors method

### Method 1: GCF of 34 and 85 by Prime Factorization

We will represent 34 and 85 as a product of their prime factors.

Prime factorization of 34 is 2 × 17

Prime factorization of 85 is 5 × 17

The common factor in the prime factorization of 34 and 85 is given by 17

GCF is the product of the factors that are common to the numbers, 34 and 85

GCF of 34 and 85 is 17

### Method 2: GCF of 34 and 85 by Listing the Common Factors

Look at the factors of 34 and 85.

Common Factors of 34 and 85: 1 and 17

The greatest common factor of 34 and 85 is 17

GCF of 34 and 85 is 17

Clearly, by both the methods we get the same answer, that is, GCF (34, 85) = 17