Prime factorization of $$$3528$$$
Your Input
Find the prime factorization of $$$3528$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3528$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3528$$$ by $$${\color{green}2}$$$: $$$\frac{3528}{2} = {\color{red}1764}$$$.
Determine whether $$$1764$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1764$$$ by $$${\color{green}2}$$$: $$$\frac{1764}{2} = {\color{red}882}$$$.
Determine whether $$$882$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$882$$$ by $$${\color{green}2}$$$: $$$\frac{882}{2} = {\color{red}441}$$$.
Determine whether $$$441$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$441$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$441$$$ by $$${\color{green}3}$$$: $$$\frac{441}{3} = {\color{red}147}$$$.
Determine whether $$$147$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$147$$$ by $$${\color{green}3}$$$: $$$\frac{147}{3} = {\color{red}49}$$$.
Determine whether $$$49$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$49$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$49$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$49$$$ by $$${\color{green}7}$$$: $$$\frac{49}{7} = {\color{red}7}$$$.
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: $$$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$$$.
Answer
The prime factorization is $$$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$$$A.