# What is the HCF of 34 and 85?

HCF or the highest common factor of two numbers 34 and 85 is the largest possible number that divides both the numbers exactly.

## Answer: HCF of 34 and 85 is 17

Let us calculate HCF of 34 and 85

## Explanation:

The highest common factor(HCF) or the greatest common factor(GCF)of two numbers is the largest possible number which divides both the numbers exactly without any remainder.

We will use the following two methods to find the HCF of 34 and 85.

- HCF of 34 and 85 by Prime factorization Method
- HCF of 34 and 85 by Listing Method

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

In this method, we represent 34 and 85 as a product of its prime numbers

Prime factorization of 34 is 2 × 17

Prime factorization of 85 is 5 × 17

Common factors of 34 and 85 are 1 and 17

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

This means HCF of 34 and 85 is 17.

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

In this method, we list all the factors of 34 and 85, then identify the common factors.

The highest among the common factors is the HCF of 34 and 85.

Factors of 34 are **1,** 2, **17,** 34

Factors of 85 are **1,** 5, **17,** 85

Common Factors of 34 and 85 are 1 and 17

The greatest common factor of 34 and 85 is 17

HCF of 34 and 85 is 17

The solution to HCF of 34 and 85 is the same as 17 and is constant for a given set of numbers.