To Find Highest Common Factor by using Division Method

This topic would discuss about finding the highest common factor of three numbers using the division method. We have learnt in our last topic about finding the highest common factor of two numbers. While doing with three numbers first we will find the highest common factor of two numbers and that highest common factor would be treated as the divisor and the third number would be treated as dividend and then we shall again do repeated division until the remainder comes zero and the divisor of the last division would be the highest common factor of three numbers. 

Steps to be followed to find the highest common factor of three numbers:

Step I: First take two numbers and find their highest common factor using the repeated long division method.

Step II: Then the highest common factor obtained in previous step is treated as divisor and the third number is treated as dividend and then again repeated long division is carried out until the remainder comes zero.

Step III: The divisor of the last division where the remainder is zero is the highest common factor of three numbers.


Here are few examples to illustrate the highest common factor of three numbers using long division method:

1. Find the H.C.F of 250, 264, and 300 using long division method

Solution:

First we will find the highest common factor of 250 and 264

To Find Highest Common Factor by using Division Method

The highest common factor of 250 and 264 is 2

Now as 2 is the highest common factor of 250 and 264 hence 2 will be treated as divisor and 300 will be the dividend for the next part of division to find H.C.F of three numbers 250, 264 and 300.

To Find Highest Common Factor by using Division Method

Since 2 is the divisor of the last division and in this division the remainder is zero

Hence, the highest common factor of 250, 264 and 300 is 2


2. Find the H.C.F of 50, 65, and 80 using long division method

Solution:

First we will find the highest common factor of 50 and 65

To Find Highest Common Factor by using Division Method

The highest common factor of 50 and 65 is 5

As, 5 is the highest common factor of 50 and 65 hence 5 will be treated as divisor and 80 the dividend for the next part of division to find the highest common factor of three numbers 50, 65 and 80

To Find Highest Common Factor by using Division Method

Now we can see that 5 is the divisor of the last division where the remainder is zero. Hence, the highest common factor of 50, 65 and 80 is 5


3. Find the H.C.F of 100, 150, and 250 using long division method

Solution:

First we will find the highest common factor of 100 and 150

To Find Highest Common Factor by using Division Method

The highest common factor of 100 and 150 is 50

Now as 50 is the highest common factor of 100 and 150 hence, 50 will be treated s the divisor and 250 will be the dividend for the next part of division

To Find Highest Common Factor by using Division Method

Here we can see that 50 is the last divisor of the division and the remainder is also zero hence, the highest common factor of 100,150 and 250 is 50

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