# Prime factorization of $4112$

The calculator will find the prime factorization of $4112$, with steps shown.

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Find the prime factorization of $4112$.

### Solution

Start with the number $2$.

Determine whether $4112$ is divisible by $2$.

It is divisible, thus, divide $4112$ by ${\color{green}2}$: $\frac{4112}{2} = {\color{red}2056}$.

Determine whether $2056$ is divisible by $2$.

It is divisible, thus, divide $2056$ by ${\color{green}2}$: $\frac{2056}{2} = {\color{red}1028}$.

Determine whether $1028$ is divisible by $2$.

It is divisible, thus, divide $1028$ by ${\color{green}2}$: $\frac{1028}{2} = {\color{red}514}$.

Determine whether $514$ is divisible by $2$.

It is divisible, thus, divide $514$ by ${\color{green}2}$: $\frac{514}{2} = {\color{red}257}$.

The prime number ${\color{green}257}$ has no other factors then $1$ and ${\color{green}257}$: $\frac{257}{257} = {\color{red}1}$.

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: $4112 = 2^{4} \cdot 257$.

The prime factorization is $4112 = 2^{4} \cdot 257$A.