Prime factorization of $$$2310$$$
Your Input
Find the prime factorization of $$$2310$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2310$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2310$$$ by $$${\color{green}2}$$$: $$$\frac{2310}{2} = {\color{red}1155}$$$.
Determine whether $$$1155$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1155$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1155$$$ by $$${\color{green}3}$$$: $$$\frac{1155}{3} = {\color{red}385}$$$.
Determine whether $$$385$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$385$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$385$$$ by $$${\color{green}5}$$$: $$$\frac{385}{5} = {\color{red}77}$$$.
Determine whether $$$77$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$77$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$77$$$ by $$${\color{green}7}$$$: $$$\frac{77}{7} = {\color{red}11}$$$.
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: $$$2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11$$$.
Answer
The prime factorization is $$$2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11$$$A.