Question

What are all the factors of 360?

Answer 1

`360 = 2 * 2 * 2 * 3 * 3 * 5 = 2^3 * 3^2 * 5`

Explanation:

If you are at loss, how to start with this kind of a task, you can always start with checking if the number can be divided by `2`.

(Reminder: all numbers which have an even last digit are dividable by `2`.)

So,

`360 = 2 * 180`.

Let's go further: `180` is dividable by `2` again:

`360 = 2 * 180 = 2 * 2 * 90`

You can divide by `2` once more:

`360 = 2 * 180 = 2 * 2 * 90 = 2 * 2 * 2 * 45`

Now, `45` has a `5` as an odd last digit, so it is not dividable by `2` anymore.
However, as the last digit is a `5`, it is can be divided by `5`:

`360 = 2 * 180 = 2 * 2 * 90 = 2 * 2 * 2 * 5 * 9`

Now, the last thing to do is determining that `9` is dividable by `3`:

`360 = 2 * 180 = 2 * 2 * 90 = 2 * 2 * 2 * 5 * 3 * 3`

`= 2^3 * 3^2 * 5`