# What is the HCF of 36, 42, and 48?

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 36, 42, and 48 is 4

Let us see how to find the HCF of 36, 42, and 48

## 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 36, 42, and 48.

- HCF of 36, 42, and 48 by Listing Method
- HCF of 36, 42, and 48 by long division 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 (36, 42, 48) by Listing the Common Factors

In this method,

- We list all the factors of 36, 42, and 48.
- Identify the common factors.
- The highest among the common factors is the GCF of 36, 42, and 48.

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

The factors of 42 are **1**, **2**, **3**, **6**, 7, 14, 21, 42

The factors of 48 are **1**, **2**, **3**, **4**, **6**, 8, **12**, 16, 24, 48

The common factors of 36, 42, and 48 are 1, 2, 3, and 6.

The greatest common factor (GCF) of 36, 42, and 48 is 6.

### Method 2: Find HCF (36, 42, 48) by long division Method

HCF of 36, 42, and 48 by division method is as follows:

- Divide 48 by 36 and check the remainder.
- Make the remainder of the above step (12) as the divisor and the divisor of the above step(36) as the dividend and perform the long division again.
- Continue till you get the remainder as 0

- Take the HCF of 48 and 36 as the divisor for the next step
- Now, continue the long division process with the common factor (48, 36) as divisor and 42 as the dividend.
- Continue till you get the remainder as 0
- The final divisor where you get the remainder as 0 is the HCF (36, 42, 48)

HCF (36, 42, 48) is the same as 6, irrespective of the method. HCF is unique and invariant for a given set of numbers.