Question

Use Euclids division algorithm to find the hcf of 867 and 255?

Answer 1

867=255 × 3 +102

255 = 102 × 2 + 51

102 = 51 × 2 + 0

so, HCF= 51.

Answer 2

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since 867 > 255,we apply the division lemma to 867 and 255 to obtain

867=255×3+102

since remainder 102≠0,we apply he division lemma to 255 and 102 to obtain

255=102×2+51

we consider, the new divisor 102 and new remainder 51, and the division lemma to obtain

102=51×2+0

since the remainder is 0,the process stops

since the divisor at this stage is 51

Therefore the HCF of 867 and 255 is 51.