Question

Use Euclid's algorithm to find HCF of 1651 &2032 express hcf in the form of 1651 m +2023n

Answer 1

we find HCF of (1651,2032) by using following steps :

Step i) Since 2032>1651 then we divide 2032 by 1651 to get quotient and remainder 381

By Euclid's division lemma,

we get :2032 =1651×1 +381.....(i)

step ii)since the remainder 381 isn't equal to the zero ,we divide 1651 by 381 to get 4 as quotient & 127 remainder.

since, by Euclid's division lemma :

381=127×3+0......(ii)

step iii)since then remainder isn't equal to the zero then,we divide 381 by 127 get 3 as a quotient & 0 as a remainder.

Therefore,By Euclid's lemma :...

381=127×3+0

The remainder is now 0,so pur procedures stops here!

Therefore,HCF (1651,2032) : 127.

__________________________

Now from (ii) we get,

1651 =381 ×4 +127

=》127=1651-381×4

=》127=1651-(2032-1651×1)×4 [from eq..1st]

=》127=1651-2032×4+1651×4

=》127=1651×5+2032×(-4)

=》127=1651×5+2032×(-4)

Hence, m=5 & n =-4.....Ans

Answer 2

Refer the attachment.

m = 5

n = -4