# Prime factorization of $1616$

The calculator will find the prime factorization of $1616$, with steps shown.

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Find the prime factorization of $1616$.

### Solution

Start with the number $2$.

Determine whether $1616$ is divisible by $2$.

It is divisible, thus, divide $1616$ by ${\color{green}2}$: $\frac{1616}{2} = {\color{red}808}$.

Determine whether $808$ is divisible by $2$.

It is divisible, thus, divide $808$ by ${\color{green}2}$: $\frac{808}{2} = {\color{red}404}$.

Determine whether $404$ is divisible by $2$.

It is divisible, thus, divide $404$ by ${\color{green}2}$: $\frac{404}{2} = {\color{red}202}$.

Determine whether $202$ is divisible by $2$.

It is divisible, thus, divide $202$ by ${\color{green}2}$: $\frac{202}{2} = {\color{red}101}$.

The prime number ${\color{green}101}$ has no other factors then $1$ and ${\color{green}101}$: $\frac{101}{101} = {\color{red}1}$.

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: $1616 = 2^{4} \cdot 101$.

The prime factorization is $1616 = 2^{4} \cdot 101$A.