Question

Use Euclid's algorithm to find the HCF of $1651$ and $2032$.

Answer 1

$1651$ and $2032$,
The given integers are $1651$ and $2032$,
Since $1651<2032$,
Apply Euclid's division algorithm to find HCF of $1651$ and $2032$
$2032=(1651\ast 1)+381$
Since the remainder $381\ne 0$

Apply Euclid's division algorithm to find HCF of $1651$ and $381$
$1651=(381\ast 4\ast 1)+127$
Since the remainder $127\ne 0$
Apply Euclid's division algorithm to $381$ and $127$
$381=(127\ast 3)+0$
Since the remainder is zero.
$\therefore$ HCF of $1651$ and $2032$ is $127$.