Prime factorization of $$$3364$$$

Find the prime factorization of $$$3364$$$.

Start with the number $$$2$$$.

Determine whether $$$3364$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3364$$$ by $$${\color{green}2}$$$: $$$\frac{3364}{2} = {\color{red}1682}$$$.

Determine whether $$$1682$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1682$$$ by $$${\color{green}2}$$$: $$$\frac{1682}{2} = {\color{red}841}$$$.

Determine whether $$$841$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$841$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$841$$$ is divisible by $$$5$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$7$$$.

Determine whether $$$841$$$ is divisible by $$$7$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$11$$$.

Determine whether $$$841$$$ is divisible by $$$11$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$13$$$.

Determine whether $$$841$$$ is divisible by $$$13$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$17$$$.

Determine whether $$$841$$$ is divisible by $$$17$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$19$$$.

Determine whether $$$841$$$ is divisible by $$$19$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$23$$$.

Determine whether $$$841$$$ is divisible by $$$23$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$29$$$.

Determine whether $$$841$$$ is divisible by $$$29$$$.

It is divisible, thus, divide $$$841$$$ by $$${\color{green}29}$$$: $$$\frac{841}{29} = {\color{red}29}$$$.

The prime number $$${\color{green}29}$$$ has no other factors then $$$1$$$ and $$${\color{green}29}$$$: $$$\frac{29}{29} = {\color{red}1}$$$.

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: $$$3364 = 2^{2} \cdot 29^{2}$$$.

The prime factorization is $$$3364 = 2^{2} \cdot 29^{2}$$$A.