Prime factorization of $$$480$$$

Find the prime factorization of $$$480$$$.

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

Determine whether $$$480$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$480$$$ by $$${\color{green}2}$$$: $$$\frac{480}{2} = {\color{red}240}$$$.

Determine whether $$$240$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$240$$$ by $$${\color{green}2}$$$: $$$\frac{240}{2} = {\color{red}120}$$$.

Determine whether $$$120$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$120$$$ by $$${\color{green}2}$$$: $$$\frac{120}{2} = {\color{red}60}$$$.

Determine whether $$$60$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$60$$$ by $$${\color{green}2}$$$: $$$\frac{60}{2} = {\color{red}30}$$$.

Determine whether $$$30$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$30$$$ by $$${\color{green}2}$$$: $$$\frac{30}{2} = {\color{red}15}$$$.

Determine whether $$$15$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$15$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$15$$$ by $$${\color{green}3}$$$: $$$\frac{15}{3} = {\color{red}5}$$$.

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: $$$480 = 2^{5} \cdot 3 \cdot 5$$$.

The prime factorization is $$$480 = 2^{5} \cdot 3 \cdot 5$$$A.