Prime factorization of $$$528$$$

Find the prime factorization of $$$528$$$.

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

Determine whether $$$528$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$528$$$ by $$${\color{green}2}$$$: $$$\frac{528}{2} = {\color{red}264}$$$.

Determine whether $$$264$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$264$$$ by $$${\color{green}2}$$$: $$$\frac{264}{2} = {\color{red}132}$$$.

Determine whether $$$132$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$132$$$ by $$${\color{green}2}$$$: $$$\frac{132}{2} = {\color{red}66}$$$.

Determine whether $$$66$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$66$$$ by $$${\color{green}2}$$$: $$$\frac{66}{2} = {\color{red}33}$$$.

Determine whether $$$33$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$33$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$33$$$ by $$${\color{green}3}$$$: $$$\frac{33}{3} = {\color{red}11}$$$.

The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.

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: $$$528 = 2^{4} \cdot 3 \cdot 11$$$.

The prime factorization is $$$528 = 2^{4} \cdot 3 \cdot 11$$$A.