Prime factorization of $$$2698$$$
Your Input
Find the prime factorization of $$$2698$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2698$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2698$$$ by $$${\color{green}2}$$$: $$$\frac{2698}{2} = {\color{red}1349}$$$.
Determine whether $$$1349$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1349$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1349$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1349$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1349$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$1349$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$1349$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$1349$$$ is divisible by $$$19$$$.
It is divisible, thus, divide $$$1349$$$ by $$${\color{green}19}$$$: $$$\frac{1349}{19} = {\color{red}71}$$$.
The prime number $$${\color{green}71}$$$ has no other factors then $$$1$$$ and $$${\color{green}71}$$$: $$$\frac{71}{71} = {\color{red}1}$$$.
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: $$$2698 = 2 \cdot 19 \cdot 71$$$.
Answer
The prime factorization is $$$2698 = 2 \cdot 19 \cdot 71$$$A.