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Question

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Use Euclid’s division algorithm to find the HFC of 867 and 255

Solution

Given integers are 867 and 255.

Clearly 867 > 255

Therefore, by applying Euclid’s division lemma to 867 and 255, we get

II. Since the remainder 102 ≠ 0, we apply division lemma to get,

III. We consider the new divisor 102 and new remainder 51 and apply division lemma to get,

The remainder at this step is zero. So, the divisor at this stage or the remainder at the previous stage i.e., 51 is the HCF of 867 and 255.

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