# What are all the factors of 360?

Mar 29, 2016

$360 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 = {2}^{3} \cdot {3}^{2} \cdot 5$

#### 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,

$360 = 2 \cdot 180$.

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

$360 = 2 \cdot 180 = 2 \cdot 2 \cdot 90$

You can divide by $2$ once more:

$360 = 2 \cdot 180 = 2 \cdot 2 \cdot 90 = 2 \cdot 2 \cdot 2 \cdot 45$

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 $5$:

$360 = 2 \cdot 180 = 2 \cdot 2 \cdot 90 = 2 \cdot 2 \cdot 2 \cdot 5 \cdot 9$

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

$360 = 2 \cdot 180 = 2 \cdot 2 \cdot 90 = 2 \cdot 2 \cdot 2 \cdot 5 \cdot 3 \cdot 3$

$= {2}^{3} \cdot {3}^{2} \cdot 5$