Question

If $a679b$ is a five digit number that is divisible by $72$ determine ${}^{\prime }{a}^{\prime }.$

Answer 1

$\Rightarrow$ For number to be divisible by $72$ ,it should be divisible by $9$ and $8.$

$\Rightarrow$ Divisibility rule of $8$ : Last $3$ digits of number should be divisible by $8$

$\Rightarrow$ $\frac{79b}{8}$ if we put $b=2$ then it get divisible by $8.$

$\therefore$ $b=2$

$\Rightarrow$ Divisibility rule of $9$ : Sum of all digits of number should be multiple of $9$ or divisible by $9$

$\Rightarrow$ $a+6+7+9+2=Multipleof9$

$\Rightarrow$ $a+24$ =multiple 0f $9$ (greater than 24)

$\Rightarrow$ $a+24=27$

$\therefore$ $a=3$