Prime factorization of $$$3177$$$

Find the prime factorization of $$$3177$$$.

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

Determine whether $$$3177$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3177$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3177$$$ by $$${\color{green}3}$$$: $$$\frac{3177}{3} = {\color{red}1059}$$$.

Determine whether $$$1059$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1059$$$ by $$${\color{green}3}$$$: $$$\frac{1059}{3} = {\color{red}353}$$$.

The prime number $$${\color{green}353}$$$ has no other factors then $$$1$$$ and $$${\color{green}353}$$$: $$$\frac{353}{353} = {\color{red}1}$$$.

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: $$$3177 = 3^{2} \cdot 353$$$.

The prime factorization is $$$3177 = 3^{2} \cdot 353$$$A.