What are all the factors of 360?

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Answer 1 · 2016-03-29T08:34:04

#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#