11+ Maths Solved Topic Wise Questions

1. HCF

The Highest Common Factor (HCF) of two or more numbers is the highest possible number which divides the given numbers completely. The highest common factor (HCF) is also called the greatest common factor (GCF).

Let's learn the different methods to find the HCF of two or more.

2. How to find HCF:

HCF of two or more numbers can be determined by using the following method:

1. By Listing Factors
2. Using Prime Factorisation

2.1 By listing Factors

This method involves making a list of each number's factors and then identifying their common factors. The highest common factor among the common factors is then identified. 

Let's use an example to better understand this approach.

Example: Find the highest common factor (HCF) of 18 and 21.

Step 01: Write down all the factors of 18 and 21

Factors of 18: 1, 2, 3, 6, 9 and 18 

Factors of 21: 1, 3, 7 and  21

Step 02: Write down the highest common factor of 18 and 21.

Common factors of the 18 and 21 is only 1 and 3.

So the Highest Common Factor of 18 and 21 is 3. 

Example: Find the highest common factor (HCF) of 24 and 36.

Step 01:  Write down all the factors of 24 and 36

Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24

Factors of 36: 1, 2, 3, 4, 6, 8, 9, 12, 18 and 36

Step 02: Write down the common factors of 24 and 36

Common factors of the 24 and 36 are 1, 2, 3, 4, 6, 8 and 12

Step 03: Select the Highest number from the common factors

So the highest common factor of 24 and 36 is 12. 

2.2 Using the Prime Factorisation

In this method first we have to do the prime factorisation of given numbers. Then we have to multiply all the prime factors that appear in either number. By doing this we will get LCM of those two numbers.

Example:1 Find the highest common factor (HCF) of 8 and 12.

Step 01: Do the prime factorisations of 8 and 12

Prime factorisation of 8 = 2 x 2 x 2 

Prime factorisation of 12 = 2 x 2 x 3 

Step 02: Write all the common prime factors of 8 and 12.

Prime factors 2 appears twice in prime factorisation of 8 and 12 so common prime factors are 2 for two times in 8 and 12.

Step 03: Multiply all the common prime factors of 8 and 12 

To find the HCF multiply the common prime factors. So HCF = 2 x 2 = 4