Prime factorization of $$$3225$$$

Find the prime factorization of $$$3225$$$.

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

Determine whether $$$3225$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3225$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3225$$$ by $$${\color{green}3}$$$: $$$\frac{3225}{3} = {\color{red}1075}$$$.

Determine whether $$$1075$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1075$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1075$$$ by $$${\color{green}5}$$$: $$$\frac{1075}{5} = {\color{red}215}$$$.

Determine whether $$$215$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$215$$$ by $$${\color{green}5}$$$: $$$\frac{215}{5} = {\color{red}43}$$$.

The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.

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: $$$3225 = 3 \cdot 5^{2} \cdot 43$$$.

The prime factorization is $$$3225 = 3 \cdot 5^{2} \cdot 43$$$A.