Question

find the HCF of 135and225?by Euclid division algorithm.​

Answer 1

Answer:

Given numbers: 135 and 225

Here, 225>135.

So, we will divide greater number by smaller number.

Divide 225 by 135.

The quotient is 1 and remainder is 90.

225=135×1+90

Divide 135 by 90

The quotient is 1 and remainder is 45.

135=90×1+45

Divide 90 by 45.

The quotient is 2 and remainder is 0.

90=2×45+0

Thus, the HCF is 45.

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Answer 2

Divide 225 and 135

Dividend = divisor × quotient + remainder

By Euclid division lemma

Given two integers a and b there exists unique integers q and r satisfying a= bq+r

0<=r< b

225=(135×1)+90

R=90 is not equal to 0

So we divide 135 and 90

135=(90×1)+45

r=45 is not equal to 0

So we divide 90 and 45

90=(45×2)+0

r=0

So we stop this process

Divisor at the last step is HCF.

Therefore HCF(135,225) is 45

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