# If $x$ is a digit such that the number $\overline{18\times71}$ is divisible by 3, find possible values of $x$.

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Given:

$x$ is a digit such that the number $\overline{18\times71}$ is divisible by 3.

To do:

We have to find the possible values of $x$.

Solution:

The number  $\overline{18\times71}$ is divisible by 3.

This implies,

The sum of its digits will also be divisible by 3.

Therefore,

$1 + 8 + x + 7+ 1$ is divisible by 3.

$17 + x$ is divisible by 3

If $x=1$, $17+1=18$ is divisible by 3.

If $x=4$, $17+4=21$ is divisible by 3.

If $x=7$, $17+7=24$ is divisible by 3.

The possible values of $x$ are $1, 4$ and $7$.

Updated on 10-Oct-2022 13:19:16