Find the digits p and q, if the number p7q6 is divisible by 24.

Given :

p7q6 is divisible by 24.

To find :

We have to find the digits p and q.

Solution :

This implies, it is divisible by both 3 and 8.

Divisibility by 8: A number is divisible by 8 if the number formed by the last 3 digits is divisible by 8.

For 7q6 to be divisible by 8,

$q = 3, 736 is divisible by 8$.

$q = 7, 776 is divisible by 8$.

Divisibility by 3: A number is divisible by 3 if the sum of the digits is divisible by 3.

If $q=3$, number is p736

Sum of the digits $= p+16$. It is divisible by 3, when $p = 2$ or $5$ or $8$.

Therefore, the number can be 2736 or 5736 or 8736.

If $q = 7$, number is p776.

Sum of the digits $= p+20$. It is divisible by 3, when $p = 1$ or $4$ or $7$.

Therefore, the number can be 1776 or 4776 or 7776.

The digits p and q can be 1 or 4 or 7 or 2 or 5 or 8 and 3 or 7 respectively.

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Updated on: 10-Oct-2022

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