Prime factorization of $$$3601$$$

Find the prime factorization of $$$3601$$$.

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

Determine whether $$$3601$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3601$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$3601$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$3601$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$3601$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$3601$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$3601$$$ by $$${\color{green}13}$$$: $$$\frac{3601}{13} = {\color{red}277}$$$.

The prime number $$${\color{green}277}$$$ has no other factors then $$$1$$$ and $$${\color{green}277}$$$: $$$\frac{277}{277} = {\color{red}1}$$$.

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: $$$3601 = 13 \cdot 277$$$.

The prime factorization is $$$3601 = 13 \cdot 277$$$A.