Prime factorization of $$$2565$$$

Find the prime factorization of $$$2565$$$.

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

Determine whether $$$2565$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2565$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2565$$$ by $$${\color{green}3}$$$: $$$\frac{2565}{3} = {\color{red}855}$$$.

Determine whether $$$855$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$855$$$ by $$${\color{green}3}$$$: $$$\frac{855}{3} = {\color{red}285}$$$.

Determine whether $$$285$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$285$$$ by $$${\color{green}3}$$$: $$$\frac{285}{3} = {\color{red}95}$$$.

Determine whether $$$95$$$ is divisible by $$$3$$$.

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

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

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: $$$2565 = 3^{3} \cdot 5 \cdot 19$$$.

The prime factorization is $$$2565 = 3^{3} \cdot 5 \cdot 19$$$A.