H.C.F. by Long Division Method
To find the H.C.F. of the given number we will follow the following steps:
- We divide the bigger number by smaller one.
- Divide smaller number in step 1 with remainder obtained in step 1.
- Divide divisor of second step with remainder obtained in step 2.
- We will continue this process till we get remainder zero and divisor obtained in end is the required H.C.F.
Let’s take few examples for this:
Example 1: Find the H.C.F. of 248 and 492?
To find the solution we will follow the following method i.e. we divide bigger number 492 by smaller one i.e. 248
So the divisor in the end was 4 so the H.C.F of the given numbers is 4
Example 2: Find the H.C.F. of 420 and 396?
To find the solution we will follow the following method i.e. we divide bigger number 420 by smaller one i.e. 396
So the divisor in the end was 12 so the H.C.F of the given numbers is 12
Some points to remember
– If H is the HCF of two numbers A and B, then H is also a factor of AX and BY, where X and Y are integers. In other words, H is also a factor of multiples of these numbers.
– If HCF (A,B) is H, then H is also the HCF of (A) and (A+B)
– If HCF (A,B) is H, then H is also the HCF of (A) and (A-B)
– If HCF (A,B) is H, then H is also the HCF of (A+B) and (A-B)
– If HCF=LCM for two numbers, then the numbers must be equal to each other.
– HCF of two or more fractions is given by:
(HCF of numerators of all the fractions) / (LCM of denominator of all the fractions)
