Prime factorization of $$$1730$$$

Find the prime factorization of $$$1730$$$.

Start with the number $$$2$$$.

Determine whether $$$1730$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1730$$$ by $$${\color{green}2}$$$: $$$\frac{1730}{2} = {\color{red}865}$$$.

Determine whether $$$865$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$865$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$865$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$865$$$ by $$${\color{green}5}$$$: $$$\frac{865}{5} = {\color{red}173}$$$.

The prime number $$${\color{green}173}$$$ has no other factors then $$$1$$$ and $$${\color{green}173}$$$: $$$\frac{173}{173} = {\color{red}1}$$$.

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: $$$1730 = 2 \cdot 5 \cdot 173$$$.

The prime factorization is $$$1730 = 2 \cdot 5 \cdot 173$$$A.