Prime factorization of $$$4506$$$

Find the prime factorization of $$$4506$$$.

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

Determine whether $$$4506$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4506$$$ by $$${\color{green}2}$$$: $$$\frac{4506}{2} = {\color{red}2253}$$$.

Determine whether $$$2253$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2253$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2253$$$ by $$${\color{green}3}$$$: $$$\frac{2253}{3} = {\color{red}751}$$$.

The prime number $$${\color{green}751}$$$ has no other factors then $$$1$$$ and $$${\color{green}751}$$$: $$$\frac{751}{751} = {\color{red}1}$$$.

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: $$$4506 = 2 \cdot 3 \cdot 751$$$.

The prime factorization is $$$4506 = 2 \cdot 3 \cdot 751$$$A.