# Prime factorization of $1312$

The calculator will find the prime factorization of $1312$, with steps shown.

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Find the prime factorization of $1312$.

### Solution

Start with the number $2$.

Determine whether $1312$ is divisible by $2$.

It is divisible, thus, divide $1312$ by ${\color{green}2}$: $\frac{1312}{2} = {\color{red}656}$.

Determine whether $656$ is divisible by $2$.

It is divisible, thus, divide $656$ by ${\color{green}2}$: $\frac{656}{2} = {\color{red}328}$.

Determine whether $328$ is divisible by $2$.

It is divisible, thus, divide $328$ by ${\color{green}2}$: $\frac{328}{2} = {\color{red}164}$.

Determine whether $164$ is divisible by $2$.

It is divisible, thus, divide $164$ by ${\color{green}2}$: $\frac{164}{2} = {\color{red}82}$.

Determine whether $82$ is divisible by $2$.

It is divisible, thus, divide $82$ by ${\color{green}2}$: $\frac{82}{2} = {\color{red}41}$.

The prime number ${\color{green}41}$ has no other factors then $1$ and ${\color{green}41}$: $\frac{41}{41} = {\color{red}1}$.

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: $1312 = 2^{5} \cdot 41$.

The prime factorization is $1312 = 2^{5} \cdot 41$A.