Prime factorization of $$$4485$$$
Your Input
Find the prime factorization of $$$4485$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4485$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$4485$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$4485$$$ by $$${\color{green}3}$$$: $$$\frac{4485}{3} = {\color{red}1495}$$$.
Determine whether $$$1495$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1495$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$1495$$$ by $$${\color{green}5}$$$: $$$\frac{1495}{5} = {\color{red}299}$$$.
Determine whether $$$299$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$299$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$299$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$299$$$ is divisible by $$$13$$$.
It is divisible, thus, divide $$$299$$$ by $$${\color{green}13}$$$: $$$\frac{299}{13} = {\color{red}23}$$$.
The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.
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: $$$4485 = 3 \cdot 5 \cdot 13 \cdot 23$$$.
Answer
The prime factorization is $$$4485 = 3 \cdot 5 \cdot 13 \cdot 23$$$A.