Prime factorization of $$$4525$$$

Find the prime factorization of $$$4525$$$.

Start with the number $$$2$$$.

Determine whether $$$4525$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$4525$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$4525$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$4525$$$ by $$${\color{green}5}$$$: $$$\frac{4525}{5} = {\color{red}905}$$$.

Determine whether $$$905$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$905$$$ by $$${\color{green}5}$$$: $$$\frac{905}{5} = {\color{red}181}$$$.

The prime number $$${\color{green}181}$$$ has no other factors then $$$1$$$ and $$${\color{green}181}$$$: $$$\frac{181}{181} = {\color{red}1}$$$.

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: $$$4525 = 5^{2} \cdot 181$$$.

The prime factorization is $$$4525 = 5^{2} \cdot 181$$$A.