Question

Find all possible values of $x$ for which the number $7x3$ is divisible by $3$. Also, find each such number.

Answer 1

For a number to be divisible by $3$, the sum of the digits of the number must be divisible by $3$.
Sum of the digits =$7+x+3$

=$10+x$
$10+x$ will be divisible by $3$ in the following cases:
Case I: $10+x=12$, or $x=2$ Thus, the number will be $723$.

Case II: $10+x=15$, or $x=5$.Thus, the number will be $753$.

Case III: $10+x=18$, or $x=8$.Thus, the number will be $783$.
So, the numbers can be $723,753$ or $783$.