# Prime factorization of $270$

The calculator will find the prime factorization of $270$, with steps shown.

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Find the prime factorization of $270$.

### Solution

Start with the number $2$.

Determine whether $270$ is divisible by $2$.

It is divisible, thus, divide $270$ by ${\color{green}2}$: $\frac{270}{2} = {\color{red}135}$.

Determine whether $135$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $135$ is divisible by $3$.

It is divisible, thus, divide $135$ by ${\color{green}3}$: $\frac{135}{3} = {\color{red}45}$.

Determine whether $45$ is divisible by $3$.

It is divisible, thus, divide $45$ by ${\color{green}3}$: $\frac{45}{3} = {\color{red}15}$.

Determine whether $15$ is divisible by $3$.

It is divisible, thus, divide $15$ by ${\color{green}3}$: $\frac{15}{3} = {\color{red}5}$.

The prime number ${\color{green}5}$ has no other factors then $1$ and ${\color{green}5}$: $\frac{5}{5} = {\color{red}1}$.

Since we have obtained $1$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $270 = 2 \cdot 3^{3} \cdot 5$.

The prime factorization is $270 = 2 \cdot 3^{3} \cdot 5$A.