Chapter 1 · Question 2

Find the HCF of $135$ and $225$ using Euclid's division algorithm.

Answer

Using Euclid's algorithm:

225=135\times1+90

,

135=90\times1+45

,

90=45\times2+0

. Therefore, HCF

=45

.

Keep dividing and carrying the remainder forward. The last non-zero remainder is

45

, so that is the HCF.

Apply Euclid's algorithm stepwise:

225=135(1)+90

;

135=90(1)+45

;

90=45(2)+0

. Since the remainder has become zero, the divisor at this stage is the HCF. Hence

\operatorname{HCF}(135,225)=45

.

Using Euclid's algorithm: $225=135\times1+90$ , $135=90\times1+45$ , $90=45\times2+0$ .