Question

Find the greatest number of $5$ digits, that will give a remainders of $5$ , when divided by $8$ and $9$ respectively?

Answer 1

Since we should get remainder $5$ when divided with $8$ or $9$ the number should be in the form of $72\left(x\right)+5$.

If, $x=1388$

$72\left(x\right)+5=72\left(1388\right)+5=99941$

$x=1389$

$72\left(x\right)+5=72\left(1389\right)+5=100013$ this is a 6 digit no

Hence, $99941$ is the greatest $5$ digit number.