Prime factorization of $$$288$$$
Your Input
Find the prime factorization of $$$288$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$288$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$288$$$ by $$${\color{green}2}$$$: $$$\frac{288}{2} = {\color{red}144}$$$.
Determine whether $$$144$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$144$$$ by $$${\color{green}2}$$$: $$$\frac{144}{2} = {\color{red}72}$$$.
Determine whether $$$72$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$72$$$ by $$${\color{green}2}$$$: $$$\frac{72}{2} = {\color{red}36}$$$.
Determine whether $$$36$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$36$$$ by $$${\color{green}2}$$$: $$$\frac{36}{2} = {\color{red}18}$$$.
Determine whether $$$18$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$18$$$ by $$${\color{green}2}$$$: $$$\frac{18}{2} = {\color{red}9}$$$.
Determine whether $$$9$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$9$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$9$$$ by $$${\color{green}3}$$$: $$$\frac{9}{3} = {\color{red}3}$$$.
The prime number $$${\color{green}3}$$$ has no other factors then $$$1$$$ and $$${\color{green}3}$$$: $$$\frac{3}{3} = {\color{red}1}$$$.
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: $$$288 = 2^{5} \cdot 3^{2}$$$.
Answer
The prime factorization is $$$288 = 2^{5} \cdot 3^{2}$$$A.