# Prime factorization of $1696$

The calculator will find the prime factorization of $1696$, with steps shown.

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Find the prime factorization of $1696$.

### Solution

Start with the number $2$.

Determine whether $1696$ is divisible by $2$.

It is divisible, thus, divide $1696$ by ${\color{green}2}$: $\frac{1696}{2} = {\color{red}848}$.

Determine whether $848$ is divisible by $2$.

It is divisible, thus, divide $848$ by ${\color{green}2}$: $\frac{848}{2} = {\color{red}424}$.

Determine whether $424$ is divisible by $2$.

It is divisible, thus, divide $424$ by ${\color{green}2}$: $\frac{424}{2} = {\color{red}212}$.

Determine whether $212$ is divisible by $2$.

It is divisible, thus, divide $212$ by ${\color{green}2}$: $\frac{212}{2} = {\color{red}106}$.

Determine whether $106$ is divisible by $2$.

It is divisible, thus, divide $106$ by ${\color{green}2}$: $\frac{106}{2} = {\color{red}53}$.

The prime number ${\color{green}53}$ has no other factors then $1$ and ${\color{green}53}$: $\frac{53}{53} = {\color{red}1}$.

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: $1696 = 2^{5} \cdot 53$.

The prime factorization is $1696 = 2^{5} \cdot 53$A.