Prime factorization of $$$3564$$$
Your Input
Find the prime factorization of $$$3564$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3564$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3564$$$ by $$${\color{green}2}$$$: $$$\frac{3564}{2} = {\color{red}1782}$$$.
Determine whether $$$1782$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1782$$$ by $$${\color{green}2}$$$: $$$\frac{1782}{2} = {\color{red}891}$$$.
Determine whether $$$891$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$891$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$891$$$ by $$${\color{green}3}$$$: $$$\frac{891}{3} = {\color{red}297}$$$.
Determine whether $$$297$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$297$$$ by $$${\color{green}3}$$$: $$$\frac{297}{3} = {\color{red}99}$$$.
Determine whether $$$99$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$99$$$ by $$${\color{green}3}$$$: $$$\frac{99}{3} = {\color{red}33}$$$.
Determine whether $$$33$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$33$$$ by $$${\color{green}3}$$$: $$$\frac{33}{3} = {\color{red}11}$$$.
The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.
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: $$$3564 = 2^{2} \cdot 3^{4} \cdot 11$$$.
Answer
The prime factorization is $$$3564 = 2^{2} \cdot 3^{4} \cdot 11$$$A.