# What is the HCF of 40, 60, and 75?

The highest common factor or in short HCF of two numbers is the largest possible number which exactly divides both the numbers leaving no remainder.

## Answer: The HCF of 40, 60, and 75 is 5.

The highest common factor(HCF) or the greatest common factor(GCF) of two numbers is the maximum among all the common factors.

## Explanation:

We will discuss two methods to calculate HCF of 40, 60, and 75.

- Calculate HCF of 40,60 and 75 by Listing the Common Factors
- Calculate HCF(40,60, 75) by Long division

### Method 1: Calculate HCF of 40,60 and 75 by Listing the Common Factors

We list all the factors of 40, 60, and 75, then determine the common factors out of that list. The highest among the common factors is the HCF of 40, 60, and 75.

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

The factors of 60 are **1,** 2, **3,** 4, **5,** 6, 10**,** 12, 15, 20**,** 30, 60

The factors of 75 are **1,** **3,** **5,** 15, 25, 75

Common Factors of 40, 60, and 75 are 1, 3, 5

The greatest of all the common factors of 40, 60, and 75 is 5

HCF of 40, 60, and 75 is 5

### Method 2: Calculate HCF(40,60, 75) by Long division

- Divide 75 by 40 and check the remainder.
- Make the remainder of the above step as the divisor and the divisor of the above step as the dividend and perform the long division again.
- Continue till you get the remainder as 0

Take the GCF of 75 and 40 as the divisor for the next step

Now, continue the long division process with the common factor(75,40) as the divisor and 16 as the dividend.

Continue till you get the remainder as 0

The final divisor where you get the remainder as 0 is the HCF(45,60,75)

HCF(45,60,75) is always the same as 4 as it is unique and invariant with the procedures to find the HCF.