Prime factorization of $$$4587$$$
Your Input
Find the prime factorization of $$$4587$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4587$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$4587$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$4587$$$ by $$${\color{green}3}$$$: $$$\frac{4587}{3} = {\color{red}1529}$$$.
Determine whether $$$1529$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1529$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1529$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1529$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$1529$$$ by $$${\color{green}11}$$$: $$$\frac{1529}{11} = {\color{red}139}$$$.
The prime number $$${\color{green}139}$$$ has no other factors then $$$1$$$ and $$${\color{green}139}$$$: $$$\frac{139}{139} = {\color{red}1}$$$.
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: $$$4587 = 3 \cdot 11 \cdot 139$$$.
Answer
The prime factorization is $$$4587 = 3 \cdot 11 \cdot 139$$$A.