Prime factorization of $$$3624$$$

Find the prime factorization of $$$3624$$$.

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

Determine whether $$$3624$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3624$$$ by $$${\color{green}2}$$$: $$$\frac{3624}{2} = {\color{red}1812}$$$.

Determine whether $$$1812$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1812$$$ by $$${\color{green}2}$$$: $$$\frac{1812}{2} = {\color{red}906}$$$.

Determine whether $$$906$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$906$$$ by $$${\color{green}2}$$$: $$$\frac{906}{2} = {\color{red}453}$$$.

Determine whether $$$453$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$453$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$453$$$ by $$${\color{green}3}$$$: $$$\frac{453}{3} = {\color{red}151}$$$.

The prime number $$${\color{green}151}$$$ has no other factors then $$$1$$$ and $$${\color{green}151}$$$: $$$\frac{151}{151} = {\color{red}1}$$$.

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: $$$3624 = 2^{3} \cdot 3 \cdot 151$$$.

The prime factorization is $$$3624 = 2^{3} \cdot 3 \cdot 151$$$A.