Question

Use Euclid's algorithm to find the HCF of $4052$ and $12576$.

Answer 1

According to the definition of Euclid's theorem,

$a=b\times q+r$ where $0\le r<b.$

Using euclid's algorithm

$12576=4052\times 3+420$
$4052=420\times 9+272$

$420=272\times 1+148$
$272=148\times 1+124$

$124=24\times 5+4$
$24=4\times 6+0$

Therefore 4 is the H.C.F of 4052 and 12576