Prime factorization of $$$3270$$$
Your Input
Find the prime factorization of $$$3270$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3270$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3270$$$ by $$${\color{green}2}$$$: $$$\frac{3270}{2} = {\color{red}1635}$$$.
Determine whether $$$1635$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1635$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1635$$$ by $$${\color{green}3}$$$: $$$\frac{1635}{3} = {\color{red}545}$$$.
Determine whether $$$545$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$545$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$545$$$ by $$${\color{green}5}$$$: $$$\frac{545}{5} = {\color{red}109}$$$.
The prime number $$${\color{green}109}$$$ has no other factors then $$$1$$$ and $$${\color{green}109}$$$: $$$\frac{109}{109} = {\color{red}1}$$$.
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: $$$3270 = 2 \cdot 3 \cdot 5 \cdot 109$$$.
Answer
The prime factorization is $$$3270 = 2 \cdot 3 \cdot 5 \cdot 109$$$A.