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HCF - Highest Common Factor

The document defines and provides examples for calculating the highest common factor (HCF) of two or more numbers. There are two methods for finding the HCF: prime factorization and division. For prime factorization, each number is written as a product of prime factors and the HCF is the product of all common prime factors. For division, the larger number is divided by the smaller number repeatedly until the remainder is zero, and the last divisor is the HCF. The HCF of more than two numbers can be found by first calculating the HCF of two numbers and then finding the HCF of the initial HCF and the third number.

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Iffath Nazneen
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710 views6 pages

HCF - Highest Common Factor

The document defines and provides examples for calculating the highest common factor (HCF) of two or more numbers. There are two methods for finding the HCF: prime factorization and division. For prime factorization, each number is written as a product of prime factors and the HCF is the product of all common prime factors. For division, the larger number is divided by the smaller number repeatedly until the remainder is zero, and the last divisor is the HCF. The HCF of more than two numbers can be found by first calculating the HCF of two numbers and then finding the HCF of the initial HCF and the third number.

Uploaded by

Iffath Nazneen
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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HCF - Highest Common Factor

The greatest number which divides each of the two or more


numbers is called HCF or Highest Common Factor. It is also
called the Greatest Common Measure(GCM) and Greatest
Common Divisor(GCD). GCM and LCM are two different
methods, whereas LCM or Least Common Multiple is used to
find the smallest common multiple of any two or more
numbers.

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.

We can find the HCF of any given numbers by using two


methods:

 by prime factorization method

 by division method
HCF By Prime Factorization Method

Follow the below-given steps to find the hcf of numbers using


prime factorization method.

Step 1: Write each number as a product of its prime factors.


This method is called here prime factorization.

Step 2: Now list the common factors of both the numbers

Step 3: The product of all common prime factors is the


HCF( use the lower power of each common factor)

Let us understand with the help of examples.

Example 1: Evaluate the HCF of 60 and 75.

Solution:

Write each number as a product of its prime factors.


2 x 2x 3 x 5 = 60

3 x 5x 5= 75

The product of all common prime factors is the HCF( use the

The common prime factors in this example are 3 & 5.


So, HCF = 3 x 5 = 15
Example 2: Find the HCF of 36, 24 and 12.

Solution:

Write each number as a product of its prime factors.


2 x 2 x 3 x 3= 36

2 x 2 x 2 x 3 = 24

2 x 2 x 3 = 12

The product of all common prime factors is the HCF

The common prime factors in this example are 2,2 & 3.

So, HCF = 2 x 2 x 3 = 12

HCF By Division Method

Example 2: Find out HCF of 36, and 24

Steps to find the HCF of any given numbers.

 Step 1: Divide larger number by smaller number first,


such as;
Larger Number/Smaller Number

 Step 2: Divide the divisor of step 1 by the remainder left.


Divisor of step 1/Remainder

 Step 3: Again divide the divisor of step 2 by the


remainder.
Divisor of step 2/Remainder

 Step 4: Repeat the process until the remainder is zero.

 Step 5: The divisor of the last step is the HCF.

How to find the HCF of 3 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.
HCF Examples

Here are a few more example to find the highest common


factors.

Example 1: Find out HCF of 30 and 45.

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 30

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

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