Prime factorization of $$$909$$$

Find the prime factorization of $$$909$$$.

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

Determine whether $$$909$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$909$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$909$$$ by $$${\color{green}3}$$$: $$$\frac{909}{3} = {\color{red}303}$$$.

Determine whether $$$303$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$303$$$ by $$${\color{green}3}$$$: $$$\frac{303}{3} = {\color{red}101}$$$.

The prime number $$${\color{green}101}$$$ has no other factors then $$$1$$$ and $$${\color{green}101}$$$: $$$\frac{101}{101} = {\color{red}1}$$$.

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: $$$909 = 3^{2} \cdot 101$$$.

The prime factorization is $$$909 = 3^{2} \cdot 101$$$A.