Use Eulid's algortim of find HCF of 1651 and 2032. Express the HCF in the form 1651m + 2032n.

Explanation

We find HCF (n 1651 , 2032) using the following steps.
Step1. Since 2032 gt 1651, we divide 2032 by 1651 to get 1 as quotient and 381 as remainder.
by Eulid's divison lemma,
we get
`2032 = 1651 xx 1 + 381 `
step 2. Since the remainder `381 ne 0` , we divide 1651 by 381 to get 4 as quotient and 127 as remainder.
by Euclid's divison lemma, we get
` 1651 = 381 xx 4 + 127`
Step3. since the remainder `127 ne 0` , we divide 381 by 127 to get 3 as quotient and 0 as remainder.
by Euclid's divison lemma, we get
` 381 = 127 xx 3 +0`
the remainder is now 0, so our proceduce stops.
HCF ( 1651 , 2032) = 127
Now from (ii) , we get
` 1651 = 381 xx 4 + 127`
` Rightarrow 127 = 1651 - 381 xx4`
` Rightarrow 127 = 1651 - ( 2032 - 1651 xx 1) xx 4`
` Rightarrow 127 = 1651 - 2032 xx 4 + 1651 xx 4`
` Rightarrow 127 = 1651 xx 5 + 2032 xx (-4)`
Hence , m =5 n=-4