Prime factorization of $$$3069$$$
Your Input
Find the prime factorization of $$$3069$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3069$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3069$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$3069$$$ by $$${\color{green}3}$$$: $$$\frac{3069}{3} = {\color{red}1023}$$$.
Determine whether $$$1023$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1023$$$ by $$${\color{green}3}$$$: $$$\frac{1023}{3} = {\color{red}341}$$$.
Determine whether $$$341$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$341$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$341$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$341$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$341$$$ by $$${\color{green}11}$$$: $$$\frac{341}{11} = {\color{red}31}$$$.
The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.
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: $$$3069 = 3^{2} \cdot 11 \cdot 31$$$.
Answer
The prime factorization is $$$3069 = 3^{2} \cdot 11 \cdot 31$$$A.