# Prime factorization of $3616$

The calculator will find the prime factorization of $3616$, with steps shown.

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Find the prime factorization of $3616$.

### Solution

Start with the number $2$.

Determine whether $3616$ is divisible by $2$.

It is divisible, thus, divide $3616$ by ${\color{green}2}$: $\frac{3616}{2} = {\color{red}1808}$.

Determine whether $1808$ is divisible by $2$.

It is divisible, thus, divide $1808$ by ${\color{green}2}$: $\frac{1808}{2} = {\color{red}904}$.

Determine whether $904$ is divisible by $2$.

It is divisible, thus, divide $904$ by ${\color{green}2}$: $\frac{904}{2} = {\color{red}452}$.

Determine whether $452$ is divisible by $2$.

It is divisible, thus, divide $452$ by ${\color{green}2}$: $\frac{452}{2} = {\color{red}226}$.

Determine whether $226$ is divisible by $2$.

It is divisible, thus, divide $226$ by ${\color{green}2}$: $\frac{226}{2} = {\color{red}113}$.

The prime number ${\color{green}113}$ has no other factors then $1$ and ${\color{green}113}$: $\frac{113}{113} = {\color{red}1}$.

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: $3616 = 2^{5} \cdot 113$.

The prime factorization is $3616 = 2^{5} \cdot 113$A.