Use Euclid’s Division Algorithm to find the HCF of III) 867 and 255

Ans. Since 867 > 255, we apply the division lemma to 867 and 255 to obtain
867 = 255 x 3 + 102

Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to obtain
255 = 102 x 2 +51
We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain
102 = 51 x 2 + 0
Since the remainder is 0, the process stops.

Since the divisor at this stage is 51,
Therefore, HCF of 867 and 255 is 51.

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