Prime factorization of $$$4575$$$

Find the prime factorization of $$$4575$$$.

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

Determine whether $$$4575$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4575$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4575$$$ by $$${\color{green}3}$$$: $$$\frac{4575}{3} = {\color{red}1525}$$$.

Determine whether $$$1525$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1525$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1525$$$ by $$${\color{green}5}$$$: $$$\frac{1525}{5} = {\color{red}305}$$$.

Determine whether $$$305$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$305$$$ by $$${\color{green}5}$$$: $$$\frac{305}{5} = {\color{red}61}$$$.

The prime number $$${\color{green}61}$$$ has no other factors then $$$1$$$ and $$${\color{green}61}$$$: $$$\frac{61}{61} = {\color{red}1}$$$.

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: $$$4575 = 3 \cdot 5^{2} \cdot 61$$$.

The prime factorization is $$$4575 = 3 \cdot 5^{2} \cdot 61$$$A.