Question

Using euclids division lemma find the hcf of 867 and 255

Answer 1

Euclid's Division Lemma =

a = bq + r

Given Numbers = 867,225

Finding HCF (Highest Common Factor) :

867 = 225×3+192

225 = 192×1+33

192=33×5+27

33=27×1+6

27=6×4+3

6=3×2+0

The required HCF is = 3

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