Prime factorization of $$$3267$$$
Your Input
Find the prime factorization of $$$3267$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3267$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3267$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$3267$$$ by $$${\color{green}3}$$$: $$$\frac{3267}{3} = {\color{red}1089}$$$.
Determine whether $$$1089$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1089$$$ by $$${\color{green}3}$$$: $$$\frac{1089}{3} = {\color{red}363}$$$.
Determine whether $$$363$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$363$$$ by $$${\color{green}3}$$$: $$$\frac{363}{3} = {\color{red}121}$$$.
Determine whether $$$121$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$121$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$121$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$121$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$121$$$ by $$${\color{green}11}$$$: $$$\frac{121}{11} = {\color{red}11}$$$.
The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.
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: $$$3267 = 3^{3} \cdot 11^{2}$$$.
Answer
The prime factorization is $$$3267 = 3^{3} \cdot 11^{2}$$$A.