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 $3$ :

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

$= 2^3 * 3^2 * 5$