Prime factorization of $$$4275$$$

Find the prime factorization of $$$4275$$$.

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

Determine whether $$$4275$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4275$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4275$$$ by $$${\color{green}3}$$$: $$$\frac{4275}{3} = {\color{red}1425}$$$.

Determine whether $$$1425$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1425$$$ by $$${\color{green}3}$$$: $$$\frac{1425}{3} = {\color{red}475}$$$.

Determine whether $$$475$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$475$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$475$$$ by $$${\color{green}5}$$$: $$$\frac{475}{5} = {\color{red}95}$$$.

Determine whether $$$95$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$95$$$ by $$${\color{green}5}$$$: $$$\frac{95}{5} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$4275 = 3^{2} \cdot 5^{2} \cdot 19$$$.

The prime factorization is $$$4275 = 3^{2} \cdot 5^{2} \cdot 19$$$A.