# Prime factorization of $1688$

The calculator will find the prime factorization of $1688$, with steps shown.

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Find the prime factorization of $1688$.

### Solution

Start with the number $2$.

Determine whether $1688$ is divisible by $2$.

It is divisible, thus, divide $1688$ by ${\color{green}2}$: $\frac{1688}{2} = {\color{red}844}$.

Determine whether $844$ is divisible by $2$.

It is divisible, thus, divide $844$ by ${\color{green}2}$: $\frac{844}{2} = {\color{red}422}$.

Determine whether $422$ is divisible by $2$.

It is divisible, thus, divide $422$ by ${\color{green}2}$: $\frac{422}{2} = {\color{red}211}$.

The prime number ${\color{green}211}$ has no other factors then $1$ and ${\color{green}211}$: $\frac{211}{211} = {\color{red}1}$.

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: $1688 = 2^{3} \cdot 211$.

The prime factorization is $1688 = 2^{3} \cdot 211$A.