# Prime factorization of $$$2904$$$

### Your Input

**Find the prime factorization of $$$2904$$$.**

### Solution

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

Determine whether $$$2904$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2904$$$ by $$${\color{green}2}$$$: $$$\frac{2904}{2} = {\color{red}1452}$$$.

Determine whether $$$1452$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1452$$$ by $$${\color{green}2}$$$: $$$\frac{1452}{2} = {\color{red}726}$$$.

Determine whether $$$726$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$726$$$ by $$${\color{green}2}$$$: $$$\frac{726}{2} = {\color{red}363}$$$.

Determine whether $$$363$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$363$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$363$$$ by $$${\color{green}3}$$$: $$$\frac{363}{3} = {\color{red}121}$$$.

Determine whether $$$121$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$121$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$121$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$121$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$121$$$ by $$${\color{green}11}$$$: $$$\frac{121}{11} = {\color{red}11}$$$.

The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.

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: $$$2904 = 2^{3} \cdot 3 \cdot 11^{2}$$$.

### Answer

**The prime factorization is $$$2904 = 2^{3} \cdot 3 \cdot 11^{2}$$$A.**