# Prime factorization of $2312$

The calculator will find the prime factorization of $2312$, with steps shown.

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Find the prime factorization of $2312$.

### Solution

Start with the number $2$.

Determine whether $2312$ is divisible by $2$.

It is divisible, thus, divide $2312$ by ${\color{green}2}$: $\frac{2312}{2} = {\color{red}1156}$.

Determine whether $1156$ is divisible by $2$.

It is divisible, thus, divide $1156$ by ${\color{green}2}$: $\frac{1156}{2} = {\color{red}578}$.

Determine whether $578$ is divisible by $2$.

It is divisible, thus, divide $578$ by ${\color{green}2}$: $\frac{578}{2} = {\color{red}289}$.

Determine whether $289$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $289$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $289$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $289$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $289$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $289$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $289$ is divisible by $17$.

It is divisible, thus, divide $289$ by ${\color{green}17}$: $\frac{289}{17} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $2312 = 2^{3} \cdot 17^{2}$.

The prime factorization is $2312 = 2^{3} \cdot 17^{2}$A.