Prime factorization of $$$2964$$$
Your Input
Find the prime factorization of $$$2964$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2964$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2964$$$ by $$${\color{green}2}$$$: $$$\frac{2964}{2} = {\color{red}1482}$$$.
Determine whether $$$1482$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1482$$$ by $$${\color{green}2}$$$: $$$\frac{1482}{2} = {\color{red}741}$$$.
Determine whether $$$741$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$741$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$741$$$ by $$${\color{green}3}$$$: $$$\frac{741}{3} = {\color{red}247}$$$.
Determine whether $$$247$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$247$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$247$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$247$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$247$$$ is divisible by $$$13$$$.
It is divisible, thus, divide $$$247$$$ by $$${\color{green}13}$$$: $$$\frac{247}{13} = {\color{red}19}$$$.
The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.
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: $$$2964 = 2^{2} \cdot 3 \cdot 13 \cdot 19$$$.
Answer
The prime factorization is $$$2964 = 2^{2} \cdot 3 \cdot 13 \cdot 19$$$A.