If 31p3 is a multiple of 3 , where 'p' is a digit find possible values of 'p'

Given: 

$31p3$ is a multiple of 3, where $p$ is a digit.

To do: 

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

Solution:

$31p3$ is a multiple of $3$.

Divisibility rule of 3:

Sum of the digits must be divisible by 3.

$\Rightarrow 3 + 1 + p + 3$ must be divisible by 3.

$\Rightarrow 7 + p$ must be divisible by 3.

If $p=2$, then $7+2=9$ is divisible by 3.

If $p=5$, then $7+5=12$ is divisible by 3.

If $p=8$, then $7+8=15$ is divisible by 3.

Therefore, the possible values of $p$ are $2, 5$ and $8$.

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Updated on: 10-Oct-2022

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