Prime factorization of $$$3604$$$

Find the prime factorization of $$$3604$$$.

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

Determine whether $$$3604$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3604$$$ by $$${\color{green}2}$$$: $$$\frac{3604}{2} = {\color{red}1802}$$$.

Determine whether $$$1802$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1802$$$ by $$${\color{green}2}$$$: $$$\frac{1802}{2} = {\color{red}901}$$$.

Determine whether $$$901$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$901$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$901$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$901$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$901$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$901$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$901$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$901$$$ by $$${\color{green}17}$$$: $$$\frac{901}{17} = {\color{red}53}$$$.

The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.

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: $$$3604 = 2^{2} \cdot 17 \cdot 53$$$.

The prime factorization is $$$3604 = 2^{2} \cdot 17 \cdot 53$$$A.