Question

If the number ${42573}^{\ast }$ is exactly divisible by $72$, then the minimum value of ${}^{\ast }$ is:

• A. $4$
• B. $5$
• C. $6$
• D. $7$
• E. $8$

Answer 1

The correct option is C $6$

$72=9\times 8$, where $9$ and $8$ are co-prime.
The minimum value of $x$ for which $73x$ is divisible by $8$ is, $x=6$.
Sum of digits in $425736=(4+2+5+7+3+6)=27$, which is divisible by $9$.
$\therefore$ Required value of ${}^{\ast }$ is $6$.