# Prime factorization of $1708$

The calculator will find the prime factorization of $1708$, with steps shown.

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Find the prime factorization of $1708$.

### Solution

Start with the number $2$.

Determine whether $1708$ is divisible by $2$.

It is divisible, thus, divide $1708$ by ${\color{green}2}$: $\frac{1708}{2} = {\color{red}854}$.

Determine whether $854$ is divisible by $2$.

It is divisible, thus, divide $854$ by ${\color{green}2}$: $\frac{854}{2} = {\color{red}427}$.

Determine whether $427$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $427$ is divisible by $3$.

Since it is not divisible, move to the next prime number.

The next prime number is $5$.

Determine whether $427$ is divisible by $5$.

Since it is not divisible, move to the next prime number.

The next prime number is $7$.

Determine whether $427$ is divisible by $7$.

It is divisible, thus, divide $427$ by ${\color{green}7}$: $\frac{427}{7} = {\color{red}61}$.

The prime number ${\color{green}61}$ has no other factors then $1$ and ${\color{green}61}$: $\frac{61}{61} = {\color{red}1}$.

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: $1708 = 2^{2} \cdot 7 \cdot 61$.

The prime factorization is $1708 = 2^{2} \cdot 7 \cdot 61$A.