Prime factorization of $$$3584$$$
Your Input
Find the prime factorization of $$$3584$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3584$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3584$$$ by $$${\color{green}2}$$$: $$$\frac{3584}{2} = {\color{red}1792}$$$.
Determine whether $$$1792$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1792$$$ by $$${\color{green}2}$$$: $$$\frac{1792}{2} = {\color{red}896}$$$.
Determine whether $$$896$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$896$$$ by $$${\color{green}2}$$$: $$$\frac{896}{2} = {\color{red}448}$$$.
Determine whether $$$448$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$448$$$ by $$${\color{green}2}$$$: $$$\frac{448}{2} = {\color{red}224}$$$.
Determine whether $$$224$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$224$$$ by $$${\color{green}2}$$$: $$$\frac{224}{2} = {\color{red}112}$$$.
Determine whether $$$112$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$112$$$ by $$${\color{green}2}$$$: $$$\frac{112}{2} = {\color{red}56}$$$.
Determine whether $$$56$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$56$$$ by $$${\color{green}2}$$$: $$$\frac{56}{2} = {\color{red}28}$$$.
Determine whether $$$28$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$28$$$ by $$${\color{green}2}$$$: $$$\frac{28}{2} = {\color{red}14}$$$.
Determine whether $$$14$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$14$$$ by $$${\color{green}2}$$$: $$$\frac{14}{2} = {\color{red}7}$$$.
The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.
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: $$$3584 = 2^{9} \cdot 7$$$.
Answer
The prime factorization is $$$3584 = 2^{9} \cdot 7$$$A.