# Prime factorization of $312$

The calculator will find the prime factorization of $312$, with steps shown.

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Find the prime factorization of $312$.

### Solution

Start with the number $2$.

Determine whether $312$ is divisible by $2$.

It is divisible, thus, divide $312$ by ${\color{green}2}$: $\frac{312}{2} = {\color{red}156}$.

Determine whether $156$ is divisible by $2$.

It is divisible, thus, divide $156$ by ${\color{green}2}$: $\frac{156}{2} = {\color{red}78}$.

Determine whether $78$ is divisible by $2$.

It is divisible, thus, divide $78$ by ${\color{green}2}$: $\frac{78}{2} = {\color{red}39}$.

Determine whether $39$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $39$ is divisible by $3$.

It is divisible, thus, divide $39$ by ${\color{green}3}$: $\frac{39}{3} = {\color{red}13}$.

The prime number ${\color{green}13}$ has no other factors then $1$ and ${\color{green}13}$: $\frac{13}{13} = {\color{red}1}$.

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: $312 = 2^{3} \cdot 3 \cdot 13$.

The prime factorization is $312 = 2^{3} \cdot 3 \cdot 13$A.