Prime factorization of $$$2210$$$
Your Input
Find the prime factorization of $$$2210$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2210$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2210$$$ by $$${\color{green}2}$$$: $$$\frac{2210}{2} = {\color{red}1105}$$$.
Determine whether $$$1105$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1105$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1105$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$1105$$$ by $$${\color{green}5}$$$: $$$\frac{1105}{5} = {\color{red}221}$$$.
Determine whether $$$221$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$221$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$221$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$221$$$ is divisible by $$$13$$$.
It is divisible, thus, divide $$$221$$$ by $$${\color{green}13}$$$: $$$\frac{221}{13} = {\color{red}17}$$$.
The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.
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: $$$2210 = 2 \cdot 5 \cdot 13 \cdot 17$$$.
Answer
The prime factorization is $$$2210 = 2 \cdot 5 \cdot 13 \cdot 17$$$A.