Prime factorization of $$$1131$$$
Your Input
Find the prime factorization of $$$1131$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1131$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1131$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1131$$$ by $$${\color{green}3}$$$: $$$\frac{1131}{3} = {\color{red}377}$$$.
Determine whether $$$377$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$377$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$377$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$377$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$377$$$ is divisible by $$$13$$$.
It is divisible, thus, divide $$$377$$$ by $$${\color{green}13}$$$: $$$\frac{377}{13} = {\color{red}29}$$$.
The prime number $$${\color{green}29}$$$ has no other factors then $$$1$$$ and $$${\color{green}29}$$$: $$$\frac{29}{29} = {\color{red}1}$$$.
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: $$$1131 = 3 \cdot 13 \cdot 29$$$.
Answer
The prime factorization is $$$1131 = 3 \cdot 13 \cdot 29$$$A.