Prime factorization of $$$1312$$$
Your Input
Find the prime factorization of $$$1312$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1312$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1312$$$ by $$${\color{green}2}$$$: $$$\frac{1312}{2} = {\color{red}656}$$$.
Determine whether $$$656$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$656$$$ by $$${\color{green}2}$$$: $$$\frac{656}{2} = {\color{red}328}$$$.
Determine whether $$$328$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$328$$$ by $$${\color{green}2}$$$: $$$\frac{328}{2} = {\color{red}164}$$$.
Determine whether $$$164$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$164$$$ by $$${\color{green}2}$$$: $$$\frac{164}{2} = {\color{red}82}$$$.
Determine whether $$$82$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$82$$$ by $$${\color{green}2}$$$: $$$\frac{82}{2} = {\color{red}41}$$$.
The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.
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: $$$1312 = 2^{5} \cdot 41$$$.
Answer
The prime factorization is $$$1312 = 2^{5} \cdot 41$$$A.