Prime factorization of $$$4532$$$
Your Input
Find the prime factorization of $$$4532$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4532$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$4532$$$ by $$${\color{green}2}$$$: $$$\frac{4532}{2} = {\color{red}2266}$$$.
Determine whether $$$2266$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2266$$$ by $$${\color{green}2}$$$: $$$\frac{2266}{2} = {\color{red}1133}$$$.
Determine whether $$$1133$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1133$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1133$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1133$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1133$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$1133$$$ by $$${\color{green}11}$$$: $$$\frac{1133}{11} = {\color{red}103}$$$.
The prime number $$${\color{green}103}$$$ has no other factors then $$$1$$$ and $$${\color{green}103}$$$: $$$\frac{103}{103} = {\color{red}1}$$$.
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: $$$4532 = 2^{2} \cdot 11 \cdot 103$$$.
Answer
The prime factorization is $$$4532 = 2^{2} \cdot 11 \cdot 103$$$A.