Prime factorization of $$$4590$$$
Your Input
Find the prime factorization of $$$4590$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4590$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$4590$$$ by $$${\color{green}2}$$$: $$$\frac{4590}{2} = {\color{red}2295}$$$.
Determine whether $$$2295$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$2295$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$2295$$$ by $$${\color{green}3}$$$: $$$\frac{2295}{3} = {\color{red}765}$$$.
Determine whether $$$765$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$765$$$ by $$${\color{green}3}$$$: $$$\frac{765}{3} = {\color{red}255}$$$.
Determine whether $$$255$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$255$$$ by $$${\color{green}3}$$$: $$$\frac{255}{3} = {\color{red}85}$$$.
Determine whether $$$85$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$85$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$85$$$ by $$${\color{green}5}$$$: $$$\frac{85}{5} = {\color{red}17}$$$.
The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.
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: $$$4590 = 2 \cdot 3^{3} \cdot 5 \cdot 17$$$.
Answer
The prime factorization is $$$4590 = 2 \cdot 3^{3} \cdot 5 \cdot 17$$$A.