Prime factorization of $$$3362$$$
Your Input
Find the prime factorization of $$$3362$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3362$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3362$$$ by $$${\color{green}2}$$$: $$$\frac{3362}{2} = {\color{red}1681}$$$.
Determine whether $$$1681$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1681$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1681$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1681$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1681$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$1681$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$1681$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$1681$$$ is divisible by $$$19$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$23$$$.
Determine whether $$$1681$$$ is divisible by $$$23$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$29$$$.
Determine whether $$$1681$$$ is divisible by $$$29$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$31$$$.
Determine whether $$$1681$$$ is divisible by $$$31$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$37$$$.
Determine whether $$$1681$$$ is divisible by $$$37$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$41$$$.
Determine whether $$$1681$$$ is divisible by $$$41$$$.
It is divisible, thus, divide $$$1681$$$ by $$${\color{green}41}$$$: $$$\frac{1681}{41} = {\color{red}41}$$$.
The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.
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: $$$3362 = 2 \cdot 41^{2}$$$.
Answer
The prime factorization is $$$3362 = 2 \cdot 41^{2}$$$A.