Prime factorization of $$$4636$$$

Find the prime factorization of $$$4636$$$.

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

Determine whether $$$4636$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4636$$$ by $$${\color{green}2}$$$: $$$\frac{4636}{2} = {\color{red}2318}$$$.

Determine whether $$$2318$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2318$$$ by $$${\color{green}2}$$$: $$$\frac{2318}{2} = {\color{red}1159}$$$.

Determine whether $$$1159$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1159$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1159$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1159$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1159$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1159$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$1159$$$ is divisible by $$$17$$$.

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

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

Determine whether $$$1159$$$ is divisible by $$$19$$$.

It is divisible, thus, divide $$$1159$$$ by $$${\color{green}19}$$$: $$$\frac{1159}{19} = {\color{red}61}$$$.

The prime number $$${\color{green}61}$$$ has no other factors then $$$1$$$ and $$${\color{green}61}$$$: $$$\frac{61}{61} = {\color{red}1}$$$.

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: $$$4636 = 2^{2} \cdot 19 \cdot 61$$$.

The prime factorization is $$$4636 = 2^{2} \cdot 19 \cdot 61$$$A.