Prime factorization of $$$3362$$$

Find the prime factorization of $$$3362$$$.

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: $$$3362 = 2 \cdot 41^{2}$$$.

The prime factorization is $$$3362 = 2 \cdot 41^{2}$$$A.