Prime factorization of $$$4396$$$
Your Input
Find the prime factorization of $$$4396$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4396$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$4396$$$ by $$${\color{green}2}$$$: $$$\frac{4396}{2} = {\color{red}2198}$$$.
Determine whether $$$2198$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2198$$$ by $$${\color{green}2}$$$: $$$\frac{2198}{2} = {\color{red}1099}$$$.
Determine whether $$$1099$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1099$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1099$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1099$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$1099$$$ by $$${\color{green}7}$$$: $$$\frac{1099}{7} = {\color{red}157}$$$.
The prime number $$${\color{green}157}$$$ has no other factors then $$$1$$$ and $$${\color{green}157}$$$: $$$\frac{157}{157} = {\color{red}1}$$$.
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: $$$4396 = 2^{2} \cdot 7 \cdot 157$$$.
Answer
The prime factorization is $$$4396 = 2^{2} \cdot 7 \cdot 157$$$A.