Prime factorization of $$$2114$$$
Your Input
Find the prime factorization of $$$2114$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2114$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2114$$$ by $$${\color{green}2}$$$: $$$\frac{2114}{2} = {\color{red}1057}$$$.
Determine whether $$$1057$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1057$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1057$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1057$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$1057$$$ by $$${\color{green}7}$$$: $$$\frac{1057}{7} = {\color{red}151}$$$.
The prime number $$${\color{green}151}$$$ has no other factors then $$$1$$$ and $$${\color{green}151}$$$: $$$\frac{151}{151} = {\color{red}1}$$$.
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: $$$2114 = 2 \cdot 7 \cdot 151$$$.
Answer
The prime factorization is $$$2114 = 2 \cdot 7 \cdot 151$$$A.