Question

# If $24x$ is a multiple of 3, where $x$ is a digit, what is the value of $x$?

Hint: If a number is divisible by 3 then it is a multiple of 3. Try to use this condition to find out the value of $x$.

It is given in the question that $24x$ is a multiple of 3.
A multiple of a number is that number multiplied by an integer.
For example if we multiply 3 by any other integer then the result will be a multiple of 3.
If we multiply 3 by 4 we will get 12. Therefore 12 is a multiple of 3.
Similarly 6, 9, 15 etc all are the multiple of 3.
Since, $24x$ is a multiple of 3, if we multiply 3 by some integer we will get $24x$.
$x$ is a digit. Any of the numerals from 0 to 9 is known as a digit.
Therefore the value of $x$ can be any number from 0 to 9.
Now see 24 is a multiple of 3. If we multiply 8 by 3 we get 24.
Since, $24x$ has a factor 3, it will be always divisible by 3 for any digit value of x.
That means $24x$ is a multiple of $x$ for any digit value of $x$.
Therefore, the value of $x$ can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Note: Generally when we take the multiple of a number we forget to consider zero as a multiple. If we multiply any number by zero we always get 0. So 0 is a multiple of every number. Don’t forget to consider zero.