Prime factorization of $$$3002$$$
Your Input
Find the prime factorization of $$$3002$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3002$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3002$$$ by $$${\color{green}2}$$$: $$$\frac{3002}{2} = {\color{red}1501}$$$.
Determine whether $$$1501$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1501$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1501$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1501$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1501$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$1501$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$1501$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$1501$$$ is divisible by $$$19$$$.
It is divisible, thus, divide $$$1501$$$ by $$${\color{green}19}$$$: $$$\frac{1501}{19} = {\color{red}79}$$$.
The prime number $$${\color{green}79}$$$ has no other factors then $$$1$$$ and $$${\color{green}79}$$$: $$$\frac{79}{79} = {\color{red}1}$$$.
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: $$$3002 = 2 \cdot 19 \cdot 79$$$.
Answer
The prime factorization is $$$3002 = 2 \cdot 19 \cdot 79$$$A.