Prime factorization of $$$2812$$$
Your Input
Find the prime factorization of $$$2812$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2812$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2812$$$ by $$${\color{green}2}$$$: $$$\frac{2812}{2} = {\color{red}1406}$$$.
Determine whether $$$1406$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1406$$$ by $$${\color{green}2}$$$: $$$\frac{1406}{2} = {\color{red}703}$$$.
Determine whether $$$703$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$703$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$703$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$703$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$703$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$703$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$703$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$703$$$ is divisible by $$$19$$$.
It is divisible, thus, divide $$$703$$$ by $$${\color{green}19}$$$: $$$\frac{703}{19} = {\color{red}37}$$$.
The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.
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: $$$2812 = 2^{2} \cdot 19 \cdot 37$$$.
Answer
The prime factorization is $$$2812 = 2^{2} \cdot 19 \cdot 37$$$A.