Prime factorization of $$$3817$$$
Your Input
Find the prime factorization of $$$3817$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3817$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3817$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$3817$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$3817$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$3817$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$3817$$$ by $$${\color{green}11}$$$: $$$\frac{3817}{11} = {\color{red}347}$$$.
The prime number $$${\color{green}347}$$$ has no other factors then $$$1$$$ and $$${\color{green}347}$$$: $$$\frac{347}{347} = {\color{red}1}$$$.
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: $$$3817 = 11 \cdot 347$$$.
Answer
The prime factorization is $$$3817 = 11 \cdot 347$$$A.