Question

HOLA !!

Use Euclid's division algorithm to find HCF of 1651 and 2032 . Express the HCF in form of 1651m + 2032 N

Answer 1

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By Euclid's Division Lemma,

=> 2032 = 1651 x 1 + 381 ---------(1)

=> 1651 = 381 x 4 + 127

=> 381 = 127 x 3 + 0

Thus HCF = 127

Now expressing part,

We have

=> 1651 = 381 x 4 + 127

=> 127 = 1651 - (381 x 4)

Now replace 381 from (1)

=> 127 = 1651 - {2032 - (1651 x 1)}4

=> 127 = 1651 - 2032(4) + 1651(4)

=> 127 = 1651(5) - 2032(4)

=> 127 = 1651m + 2032n where m = 5 and n = - 4

Verification

=> 1651(5) = 8255
=> 2032(4) = 8128

Thus 8255 - 8128 = 127

Hence Verified also

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Answer 2

Hope this helps You....