Prime factorization of $$$423$$$
Your Input
Find the prime factorization of $$$423$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$423$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$423$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$423$$$ by $$${\color{green}3}$$$: $$$\frac{423}{3} = {\color{red}141}$$$.
Determine whether $$$141$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$141$$$ by $$${\color{green}3}$$$: $$$\frac{141}{3} = {\color{red}47}$$$.
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: $$$423 = 3^{2} \cdot 47$$$.
Answer
The prime factorization is $$$423 = 3^{2} \cdot 47$$$A.