Prime factorization of $$$3573$$$

Find the prime factorization of $$$3573$$$.

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

Determine whether $$$3573$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3573$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3573$$$ by $$${\color{green}3}$$$: $$$\frac{3573}{3} = {\color{red}1191}$$$.

Determine whether $$$1191$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1191$$$ by $$${\color{green}3}$$$: $$$\frac{1191}{3} = {\color{red}397}$$$.

The prime number $$${\color{green}397}$$$ has no other factors then $$$1$$$ and $$${\color{green}397}$$$: $$$\frac{397}{397} = {\color{red}1}$$$.

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: $$$3573 = 3^{2} \cdot 397$$$.

The prime factorization is $$$3573 = 3^{2} \cdot 397$$$A.