Prime factorization of $$$1533$$$
Your Input
Find the prime factorization of $$$1533$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1533$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1533$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1533$$$ by $$${\color{green}3}$$$: $$$\frac{1533}{3} = {\color{red}511}$$$.
Determine whether $$$511$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$511$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$511$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$511$$$ by $$${\color{green}7}$$$: $$$\frac{511}{7} = {\color{red}73}$$$.
The prime number $$${\color{green}73}$$$ has no other factors then $$$1$$$ and $$${\color{green}73}$$$: $$$\frac{73}{73} = {\color{red}1}$$$.
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: $$$1533 = 3 \cdot 7 \cdot 73$$$.
Answer
The prime factorization is $$$1533 = 3 \cdot 7 \cdot 73$$$A.