# Highest Common Factor(HCF)

The greatest number which divides each of the two or more numbers is called the Highest Common Factor(HCF). It is also called the Greatest Common Measure(GCM) and Greatest Common Divisor(GCD). HCM and LCM are different.

Example: The Highest common factor of 60 and 75 is 15 because 15 is the largest number which can divide both 60 and 75 exactly.

There’s another way to find out HCF

• by using prime factorization method

or

• by dividing the numbers or division method.

## How to Calculate HCF using prime factorization method

 Write each number as a product of its prime factors The product of all common prime factors is the HCF( use the lowes power of each common factor)

Question 1: Evaluate the HCF of 60 and 75

 Write each number as a product of its prime factors. 22 x 3 x 5 = 60 3 x 52 = 75 The product of all common prime factors is the HCF( use the lowes power of each common factor) The common prime factors in this example are 3 & 5. The lowest power of 3 is 3 and 5 is 5. So, HCF = 3 x 5 = 15

Question 2: Evaluate the HCF of 36, 24 and 12.

 Write each number as a product of its prime factors. 22 x 32 = 36 23 x 3 = 24 22 x 3 = 12 The product of all common prime factors is the HCF( use the lowes power of each common factor) The common prime factors in this example are 2 & 3. The lowest power of 2 is 22 and 3 is 3. So, HCF = 22 x 3 = 12

Question 3: Evaluate the HCF of 36, 27 and 80

 Write each number as a product of its prime factors. 22 x 32 = 36 33 = 27 24 x 5 = 80 The product of all common prime factors is the HCF( use the lowes power of each common factor) The common prime factors in this example are none. So, HCF is 1.

## How to calculate HCF Using Dividing the Numbers Method

### Shortcut method to find the HCF.

 Line the given numbers horizontally by separating it with commas. Find the small prime number and divide the given number by the same. It should exactly divide the given numbers. (Write in the left side). Now below the first line, write the quotients. Till you reach the stage when no coprime factor exists for all numbers, keep repeating the process. We will get the common prime factors as the factors in the left-hand side divides all the numbers exactly. The product of these common prime factors is the HCF.

Problem 1: Evaluate the HCF of 60 and 75

As we can note that the mentioned prime factors in the left side divide all the numbers exactly and so, they all are common prime factors. We have no common prime factor for the numbers remained at the bottom.

So, HCF = 3 × 5 = 15.

Example 2: Find out HCF of 36, 24 and 12

HCF = 2 × 2 × 3 = 12.

Example 3: Find out HCF of 36, 24 and 48

HCF = 2 × 2 × 3 = 12.

## Division method to find the HCF (Shortcut method)

Steps to find the HCF of any given numbers.

 1) $\frac{larger number}{smaller number}$ 2) $\frac{Divisor of step 1}{Remainder}$ 3) $\frac{Divisor of step 2}{Remainder}$… Continue this till R = 0(Zero). 4) The divisor of the last step is HCF.

How to find the HCF of 3 given numbers.

 1) Calculate the HCF of 2 numbers. 2) Then Find the HCF of 3rd number and the HCF found in step 1. 3) The HCF you got in step 2 will be the HCF of the 3 numbers.

The above steps can also be used to find the HCF of more than 3 numbers.

Example 1: Find out HCF of 60 and 75

So, the HCF of 30 and 45 is 15.

Example 2: Find out HCF of 12 and 36

So, HCF of 12 and 36 = 12

Example 3: Find out HCF of 9, 27, and 48

Take any two numbers and find out their HCF first. Say, let’s find out HCF of 9 and 27 initially.

So, HCF of 9 and 27 = 9

HCF of 9 ,27, 30

= HCF of [(HCF of 9, 27) and 30

= HCF of [9 and 30]

Hence, HCF of 9 ,27, 30 = 3

Example 4: Find out HCF of 5 and 7

Hence HCF of 5 and 7 = 1