Prime factorization of $$$4825$$$

Find the prime factorization of $$$4825$$$.

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

Determine whether $$$4825$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4825$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$4825$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$4825$$$ by $$${\color{green}5}$$$: $$$\frac{4825}{5} = {\color{red}965}$$$.

Determine whether $$$965$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$965$$$ by $$${\color{green}5}$$$: $$$\frac{965}{5} = {\color{red}193}$$$.

The prime number $$${\color{green}193}$$$ has no other factors then $$$1$$$ and $$${\color{green}193}$$$: $$$\frac{193}{193} = {\color{red}1}$$$.

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: $$$4825 = 5^{2} \cdot 193$$$.

The prime factorization is $$$4825 = 5^{2} \cdot 193$$$A.