Question

Find the remainder when a numbers divided by 7?

Answer 1

A few thoughts...

Explanation:

If I understand correctly, you are wondering if there is a shortcut method as there is for checking divisibility by `2`, `3` or `5`.

There is nothing as neat for finding the remainder when dividing by `7`, but there are some methods people use.

Note that if you subtract any multiple of `7` from a number then the remainder is unchanged.

So we can just start at the left hand side of a number, subtracting the largest multiple of `7` we can and repeating until we are left with a number in the range `0` to `6`.

For example, given `1234`:

• Take `7` from `12` to get `color(blue)(5)34`
• Take `49` from `53` to get `color(blue)(4)4`
• Take `42` from `44` to get `color(blue)(2)`

This is like long division, but you don't need to remember the quotient - just the running remainder and the remaining digits.