# What is the HCF of 24, 36, and 40?

The greatest common factor or highest common factor of any set of numbers is the largest possible number which divides both the numbers exactly.

## Answer: HCF of 24, 36, and 40 is 4

Let us see how to find the HCF of 24, 36, and 40

## Explanation:

The highest common factor(HCF) 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 24, 36, and 40.

- HCF of 24, 36, and 40 by Listing Method
- HCF of 24, 36, and 40 by Prime factorization Method

The largest possible number which divides both the numbers exactly without any remainder is the greatest common factor of two numbers. It is also called the highest common factor or the greatest common divisor.

### Method 1:** **Find HCF (24, 36, 40) by Listing the Common Factors

In this method,

We list all the factors of 24, 36, and 40 and then identify the common factors.

The highest among the common factors is the HCF of 24, 36, and 40.

The factors of 24 are **1**, **2**, **3**, **4**, **6**, **8**, **12**, 24

The factors of 36 are, **1**, **2**, **3**, **4**, **6**, 9, **12**, 18, 36

The factors of 40 are **1**, **2**, **4**, 5, **8**, 10, 20, 40

The common factors of 24, 36, and 40 are 1, 2 and 4

The greatest common factor (GCF) or the highest common factor (HCF) of 24, 36, and 40 is 4

### Method 2: Find HCF (24, 36, 40) by Prime factorization Method

In this method of prime factorization, we express the given numbers as a product of the primes.

The prime factorization of 24 is 2 × 2 × 2 × 3

The prime factorization of 36 is 2 × 2 × 3 × 3

The prime factorization of 40 is 2 × 2 × 2 × 5

The HCF is the product of such common prime factors.

HCF (24, 36, 40) is 2 × 2 = 4.

HCF (24, 36, 40) is the same as 4, irrespective of the method. HCF is unique for a given set of numbers.