Prime factorization of $$$3450$$$
Your Input
Find the prime factorization of $$$3450$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3450$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3450$$$ by $$${\color{green}2}$$$: $$$\frac{3450}{2} = {\color{red}1725}$$$.
Determine whether $$$1725$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1725$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$1725$$$ by $$${\color{green}3}$$$: $$$\frac{1725}{3} = {\color{red}575}$$$.
Determine whether $$$575$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$575$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$575$$$ by $$${\color{green}5}$$$: $$$\frac{575}{5} = {\color{red}115}$$$.
Determine whether $$$115$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$115$$$ by $$${\color{green}5}$$$: $$$\frac{115}{5} = {\color{red}23}$$$.
The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.
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: $$$3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23$$$.
Answer
The prime factorization is $$$3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23$$$A.