Prime factorization of $$$3165$$$
Your Input
Find the prime factorization of $$$3165$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3165$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3165$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$3165$$$ by $$${\color{green}3}$$$: $$$\frac{3165}{3} = {\color{red}1055}$$$.
Determine whether $$$1055$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1055$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$1055$$$ by $$${\color{green}5}$$$: $$$\frac{1055}{5} = {\color{red}211}$$$.
The prime number $$${\color{green}211}$$$ has no other factors then $$$1$$$ and $$${\color{green}211}$$$: $$$\frac{211}{211} = {\color{red}1}$$$.
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: $$$3165 = 3 \cdot 5 \cdot 211$$$.
Answer
The prime factorization is $$$3165 = 3 \cdot 5 \cdot 211$$$A.