Prime factorization of $$$405$$$

Find the prime factorization of $$$405$$$.

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

Determine whether $$$405$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$405$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$405$$$ by $$${\color{green}3}$$$: $$$\frac{405}{3} = {\color{red}135}$$$.

Determine whether $$$135$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$135$$$ by $$${\color{green}3}$$$: $$$\frac{135}{3} = {\color{red}45}$$$.

Determine whether $$$45$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$45$$$ by $$${\color{green}3}$$$: $$$\frac{45}{3} = {\color{red}15}$$$.

Determine whether $$$15$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$15$$$ by $$${\color{green}3}$$$: $$$\frac{15}{3} = {\color{red}5}$$$.

The prime number $$${\color{green}5}$$$ has no other factors then $$$1$$$ and $$${\color{green}5}$$$: $$$\frac{5}{5} = {\color{red}1}$$$.

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: $$$405 = 3^{4} \cdot 5$$$.

The prime factorization is $$$405 = 3^{4} \cdot 5$$$A.