# Prime factorization of $4016$

The calculator will find the prime factorization of $4016$, with steps shown.

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Find the prime factorization of $4016$.

### Solution

Start with the number $2$.

Determine whether $4016$ is divisible by $2$.

It is divisible, thus, divide $4016$ by ${\color{green}2}$: $\frac{4016}{2} = {\color{red}2008}$.

Determine whether $2008$ is divisible by $2$.

It is divisible, thus, divide $2008$ by ${\color{green}2}$: $\frac{2008}{2} = {\color{red}1004}$.

Determine whether $1004$ is divisible by $2$.

It is divisible, thus, divide $1004$ by ${\color{green}2}$: $\frac{1004}{2} = {\color{red}502}$.

Determine whether $502$ is divisible by $2$.

It is divisible, thus, divide $502$ by ${\color{green}2}$: $\frac{502}{2} = {\color{red}251}$.

The prime number ${\color{green}251}$ has no other factors then $1$ and ${\color{green}251}$: $\frac{251}{251} = {\color{red}1}$.

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: $4016 = 2^{4} \cdot 251$.

The prime factorization is $4016 = 2^{4} \cdot 251$A.