Prime factorization of $$$4606$$$
Your Input
Find the prime factorization of $$$4606$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4606$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$4606$$$ by $$${\color{green}2}$$$: $$$\frac{4606}{2} = {\color{red}2303}$$$.
Determine whether $$$2303$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$2303$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$2303$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$2303$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$2303$$$ by $$${\color{green}7}$$$: $$$\frac{2303}{7} = {\color{red}329}$$$.
Determine whether $$$329$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$329$$$ by $$${\color{green}7}$$$: $$$\frac{329}{7} = {\color{red}47}$$$.
The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.
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: $$$4606 = 2 \cdot 7^{2} \cdot 47$$$.
Answer
The prime factorization is $$$4606 = 2 \cdot 7^{2} \cdot 47$$$A.