# Prime factorization of $120$

The calculator will find the prime factorization of $120$, with steps shown.

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### Your Input

Find the prime factorization of $120$.

### Solution

Start with the number $2$.

Determine whether $120$ is divisible by $2$.

It is divisible, thus, divide $120$ by ${\color{green}2}$: $\frac{120}{2} = {\color{red}60}$.

Determine whether $60$ is divisible by $2$.

It is divisible, thus, divide $60$ by ${\color{green}2}$: $\frac{60}{2} = {\color{red}30}$.

Determine whether $30$ is divisible by $2$.

It is divisible, thus, divide $30$ by ${\color{green}2}$: $\frac{30}{2} = {\color{red}15}$.

Determine whether $15$ is divisible by $2$.

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

The next prime number is $3$.

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: $120 = 2^{3} \cdot 3 \cdot 5$.

### Answer

The prime factorization is $120 = 2^{3} \cdot 3 \cdot 5$A.