Prime factorization of $$$3806$$$
Your Input
Find the prime factorization of $$$3806$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3806$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3806$$$ by $$${\color{green}2}$$$: $$$\frac{3806}{2} = {\color{red}1903}$$$.
Determine whether $$$1903$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1903$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1903$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1903$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1903$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$1903$$$ by $$${\color{green}11}$$$: $$$\frac{1903}{11} = {\color{red}173}$$$.
The prime number $$${\color{green}173}$$$ has no other factors then $$$1$$$ and $$${\color{green}173}$$$: $$$\frac{173}{173} = {\color{red}1}$$$.
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: $$$3806 = 2 \cdot 11 \cdot 173$$$.
Answer
The prime factorization is $$$3806 = 2 \cdot 11 \cdot 173$$$A.