Prime factorization of $$$4225$$$
Your Input
Find the prime factorization of $$$4225$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4225$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$4225$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$4225$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$4225$$$ by $$${\color{green}5}$$$: $$$\frac{4225}{5} = {\color{red}845}$$$.
Determine whether $$$845$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$845$$$ by $$${\color{green}5}$$$: $$$\frac{845}{5} = {\color{red}169}$$$.
Determine whether $$$169$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$169$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$169$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$169$$$ is divisible by $$$13$$$.
It is divisible, thus, divide $$$169$$$ by $$${\color{green}13}$$$: $$$\frac{169}{13} = {\color{red}13}$$$.
The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.
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: $$$4225 = 5^{2} \cdot 13^{2}$$$.
Answer
The prime factorization is $$$4225 = 5^{2} \cdot 13^{2}$$$A.