Question

Find the quotient and the remainder when each of the following number is divided by $13$:
$8,31,44,85,1220,2011$

Answer 1

$Fast$ $Approach$ to find quotient and remainder is

Splitting a Number into Two Parts such as

$\Rightarrow 44=39+5=13\times 3+5$ therefore $q=3$ and $r=5$

Similarly we can Split other numbers

in case of $8$,

$\Rightarrow 8=13\times 0+8$ therefore $q=0$ and $r=8$

Repeating Above Technique

$\Rightarrow 31=13\times 2+5\Rightarrow q=2$ and $r=5$

$\Rightarrow 85=13\times 7+7\Rightarrow q=7$ and $r=7$

$\Rightarrow 1220=13\times 93+11\Rightarrow q=93$ and $r=11$

$\Rightarrow 2011=13\times 154+9\Rightarrow q=154$ and $r=9$