# What is the HCF of 14 and 21?

The highest common factor(HCF) of two numbers 14 and 21 is the largest whole number which divides both the numbers exactly without leaving any remainder.

## Answer: HCF of 14 and 21 is 7

let us see how to find the HCF using different methods.

## Explanation:

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

## Methods to find HCF of 14 and 21

- Prime factorization
- Listing the common factors

### Method 1: HCF of 14 and 21 by Prime Factorization

In this method, we represent 14 and 21 as a product of its prime numbers

Prime factorization of 14 is 2 × 7

Prime factorization of 21 is 3 × 7

Common factor = 7

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

HCF(14,21) is 7

### Method 2: HCF of 14 and 21 by Listing the Common Factors

In this method, we identify the common factors from the list of all the factors of 14 and 21.

The highest among the common factors is the HCF of 14 and 21.

The factors of 14 are 1, 2, 7, 14.

The factors of 21 are 1, 3, 7, 21.

Common Factors of 14 and 21: 1, 7.

The largest of all the listed common factors is 7

HCF of 14 and 21 is 7

The solution to our question is independent of the method we choose. HCF of 14 and 21 remain the same.