Question

Find $q$ and $r$ for the following pairs of positive integers $a$ and $b$ satisfying $a=bq+r$.

(1) $a=13,b=3$

(2) $a=8,b=80$

(3) $a=125,b=5$

(4) $a=132,b=11$.

Answer 1

1) $a=13,b=3$

$a=bq+r$

$13=3\times 4+1$

$\therefore q=4$ and $r=1$

2) $a=8,b=80$

$80=8\times 10+0$

$\therefore q=10$ and $r=0$

3) $a=125,b=5$

$125=5\times 25+0$

$\therefore q=25$ and $r=0$

4) $a=132,b=11$

$132=11\times 12+0$

$\therefore q=12$ and $r=0$