Question

use Euclid division algorithm to find the
HCF of 56 and 88.
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Answer 1

$\huge\text{\underline{Answer}}$

$\bold{Euclid Division Lemma }$

According to Euclid division algorithm a and b are two positive integer such that a>b when a is divided by b their exist an unique integer q as quoteint and r as remainder.

Let a = 88 and b = 56

by using euclid division algorithm

$\boxed{a = bq + r }$

where r is remainder and q is quotient.

$\implies$ $\bold{88 = 56 × 1 + 32}$

$\implies$ $\bold{56 = 32 × 1 + 24}$

$\implies$ $\bold{32 = 24 × 1 + 8}$

$\implies$ $\bold{24 = 8 × 3 + 0 }$

hence,at this step the remainder come is 0.

Therefore the HCF will be 8.