Prime factorization of $$$3170$$$

Find the prime factorization of $$$3170$$$.

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.