Question

Find the HCF of 225 and 135 using Euclid's Division Lemma.

Explain step by step the process of solving this.

Points : 15 ☺

Answer 1

Here 225 is greater than 135. We always divide greater number with the smaller one.
Divide 225 by 135 we get 1 quotient and 90 as remainder so that
225=135*1+90
Divide 135 by 90 we get 1 quotient and 45 as remainder so we can write it as
90=2*45+0
As there are no remainder so 45 is our HCF

Answer 2

according to Euclid's Divison method ,
a = br + c

135 )225( 1
135
==========
90

hence, we write this according to Euclid theorem ,
225 = 135 x 1 + 90

again ,
90)135( 1
90
========
45


write a/c to Euclid theorem ,
135 = 90 x 1 + 45

again,
45)90( 2
90
=========
00
a/c to Euclid theorem ,
90 = 2 x 45

hence, 45 is HCF of (225 , 135 )

================================

another way of Euclid theorem ,

factors of 225 = 5 x 5 x 3 x 3
facotors of 135 = 5 x 3 x 3 x 3

we know,
HCF is the Highest common factors of all given numbers

so, common factor of 225 and 135 = 5 x 3 x 3 = 45

so, HCF of (225 , 135) = common factors of (225 , 135) = 45