Prime factorization of $$$4632$$$

Find the prime factorization of $$$4632$$$.

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

Determine whether $$$4632$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4632$$$ by $$${\color{green}2}$$$: $$$\frac{4632}{2} = {\color{red}2316}$$$.

Determine whether $$$2316$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2316$$$ by $$${\color{green}2}$$$: $$$\frac{2316}{2} = {\color{red}1158}$$$.

Determine whether $$$1158$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1158$$$ by $$${\color{green}2}$$$: $$$\frac{1158}{2} = {\color{red}579}$$$.

Determine whether $$$579$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$579$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$579$$$ by $$${\color{green}3}$$$: $$$\frac{579}{3} = {\color{red}193}$$$.

The prime number $$${\color{green}193}$$$ has no other factors then $$$1$$$ and $$${\color{green}193}$$$: $$$\frac{193}{193} = {\color{red}1}$$$.

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: $$$4632 = 2^{3} \cdot 3 \cdot 193$$$.

The prime factorization is $$$4632 = 2^{3} \cdot 3 \cdot 193$$$A.