Prime factorization of $$$3014$$$
Your Input
Find the prime factorization of $$$3014$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3014$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3014$$$ by $$${\color{green}2}$$$: $$$\frac{3014}{2} = {\color{red}1507}$$$.
Determine whether $$$1507$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1507$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1507$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1507$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1507$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$1507$$$ by $$${\color{green}11}$$$: $$$\frac{1507}{11} = {\color{red}137}$$$.
The prime number $$${\color{green}137}$$$ has no other factors then $$$1$$$ and $$${\color{green}137}$$$: $$$\frac{137}{137} = {\color{red}1}$$$.
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: $$$3014 = 2 \cdot 11 \cdot 137$$$.
Answer
The prime factorization is $$$3014 = 2 \cdot 11 \cdot 137$$$A.