# Prime factorization of $3112$

The calculator will find the prime factorization of $3112$, with steps shown.

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Find the prime factorization of $3112$.

### Solution

Start with the number $2$.

Determine whether $3112$ is divisible by $2$.

It is divisible, thus, divide $3112$ by ${\color{green}2}$: $\frac{3112}{2} = {\color{red}1556}$.

Determine whether $1556$ is divisible by $2$.

It is divisible, thus, divide $1556$ by ${\color{green}2}$: $\frac{1556}{2} = {\color{red}778}$.

Determine whether $778$ is divisible by $2$.

It is divisible, thus, divide $778$ by ${\color{green}2}$: $\frac{778}{2} = {\color{red}389}$.

The prime number ${\color{green}389}$ has no other factors then $1$ and ${\color{green}389}$: $\frac{389}{389} = {\color{red}1}$.

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: $3112 = 2^{3} \cdot 389$.

The prime factorization is $3112 = 2^{3} \cdot 389$A.