Question

Find the largest number that divides $455$ and $42$ with the help of division algorithm.

Answer 1

i) Start with the larger integer$,455$
$42\left)455\right(10\to$ quotient
420
$35\to$ remainder $\therefore 455=(42\times 10)+35$ (By Euclid's lemma)
ii) Consider $42÷35$ iii) Consider $35÷7$
$35\left)42\right(1$ $7\left)35\right(5$
35 35
7 00
$\therefore 42=(35\times 1)+7$ $\therefore 35=(7\times 5)+0$

$\Rightarrow HCF(455,42)=HCF(42,35)=HCF(35,7)=7$

$\therefore 7$ is the largest number that divides $455$ and $42$.