Chapter 1 · Question 2

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

Answer Revealed

Direct 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: $225=135\times1+90$ , $135=90\times1+45$ , $90=45\times2+0$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

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