Question

Use euclid's division algorithm to find the hcf of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255

Answer 1

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Answer 2

Answer:

Ans. (i) 135 and 225

We have 225 > 135,

So, we apply the division lemma to 225 and 135 to obtain

Here remainder 90 ≠ 0, we apply the division lemma again to 135 and 90 to obtain

We consider the new divisor 90 and new remainder 45 ≠ 0, and apply the division lemma to obtain

Since at this time the remainder is zero, the process is stopped.

The divisor at this stage is 45

Therefore, the HCF of 135 and 225 is 45.

(ii) 196 and 38220

We have 38220 > 196,

So, we apply the division lemma to 38220 and 196 to obtain

As the remainder is zero, the process stops.

The divisor at this stage is 196,

Therefore, HCF of 196 and 38220 is 196.

(iii) 867 and 255

We have 867 > 255,

So, we apply the division lemma to 867 and 255 to obtain

Here remainder 102 ≠ 0, we apply the division lemma again to 255 and 102 to obtain

Here remainder 51 ≠ 0, we apply the division lemma again to 102 and 51 to obtain

As the remainder is zero, the process stops.

The divisor at this stage is 51,

Therefore, HCF of 867 and 255 is 51.