Prime factorization of $$$2205$$$
Your Input
Find the prime factorization of $$$2205$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2205$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$2205$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$2205$$$ by $$${\color{green}3}$$$: $$$\frac{2205}{3} = {\color{red}735}$$$.
Determine whether $$$735$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$735$$$ by $$${\color{green}3}$$$: $$$\frac{735}{3} = {\color{red}245}$$$.
Determine whether $$$245$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$245$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$245$$$ by $$${\color{green}5}$$$: $$$\frac{245}{5} = {\color{red}49}$$$.
Determine whether $$$49$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$49$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$49$$$ by $$${\color{green}7}$$$: $$$\frac{49}{7} = {\color{red}7}$$$.
The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.
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: $$$2205 = 3^{2} \cdot 5 \cdot 7^{2}$$$.
Answer
The prime factorization is $$$2205 = 3^{2} \cdot 5 \cdot 7^{2}$$$A.