Question

If $A679B$ is a $5$ digit number is divisible by $72$ find ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$?

Answer 1

First we have to break $72$ into factors $9,8$
Now,
$\left(i\right)$ Divisibility Rule of 8 is that the last three digits should be divisible by 8
and
$\left(ii\right)$ Divisibility Rule of 9 is that the sum of digits must be divisible by 9
So, $79B$ must be divisible by 8 and only $B=2$ is satisfying the condition
Now, using $\left(ii\right)$ we get, $A+6+7+9+2=9\alpha$ (multiple of $9$)
$A=9\alpha -24$ only $\alpha =3$ is satisfying by hit and trial method
So. $A=27-24=3$
Therefore, $A=3,B=2$