Prime factorization of $$$300$$$

Find the prime factorization of $$$300$$$.

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

Determine whether $$$300$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$300$$$ by $$${\color{green}2}$$$: $$$\frac{300}{2} = {\color{red}150}$$$.

Determine whether $$$150$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$150$$$ by $$${\color{green}2}$$$: $$$\frac{150}{2} = {\color{red}75}$$$.

Determine whether $$$75$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$75$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$75$$$ by $$${\color{green}3}$$$: $$$\frac{75}{3} = {\color{red}25}$$$.

Determine whether $$$25$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$25$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$25$$$ by $$${\color{green}5}$$$: $$$\frac{25}{5} = {\color{red}5}$$$.

The prime number $$${\color{green}5}$$$ has no other factors then $$$1$$$ and $$${\color{green}5}$$$: $$$\frac{5}{5} = {\color{red}1}$$$.

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: $$$300 = 2^{2} \cdot 3 \cdot 5^{2}$$$.

The prime factorization is $$$300 = 2^{2} \cdot 3 \cdot 5^{2}$$$A.