##360 = 2 * 2 * 2 * 3 * 3 * 5 = 2^3 * 3^2 * 5##
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##