# Prime factorization of $3170$

The calculator will find the prime factorization of $3170$, with steps shown.

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Find the prime factorization of $3170$.

### Solution

Start with the number $2$.

Determine whether $3170$ is divisible by $2$.

It is divisible, thus, divide $3170$ by ${\color{green}2}$: $\frac{3170}{2} = {\color{red}1585}$.

Determine whether $1585$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1585$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1585$ is divisible by $5$.

It is divisible, thus, divide $1585$ by ${\color{green}5}$: $\frac{1585}{5} = {\color{red}317}$.

The prime number ${\color{green}317}$ has no other factors then $1$ and ${\color{green}317}$: $\frac{317}{317} = {\color{red}1}$.

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: $3170 = 2 \cdot 5 \cdot 317$.

The prime factorization is $3170 = 2 \cdot 5 \cdot 317$A.