Prime factorization of $$$2853$$$
Your Input
Find the prime factorization of $$$2853$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2853$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$2853$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$2853$$$ by $$${\color{green}3}$$$: $$$\frac{2853}{3} = {\color{red}951}$$$.
Determine whether $$$951$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$951$$$ by $$${\color{green}3}$$$: $$$\frac{951}{3} = {\color{red}317}$$$.
The prime number $$${\color{green}317}$$$ has no other factors then $$$1$$$ and $$${\color{green}317}$$$: $$$\frac{317}{317} = {\color{red}1}$$$.
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: $$$2853 = 3^{2} \cdot 317$$$.
Answer
The prime factorization is $$$2853 = 3^{2} \cdot 317$$$A.