Prime factorization of $$$1904$$$

Find the prime factorization of $$$1904$$$.

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

Determine whether $$$1904$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1904$$$ by $$${\color{green}2}$$$: $$$\frac{1904}{2} = {\color{red}952}$$$.

Determine whether $$$952$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$952$$$ by $$${\color{green}2}$$$: $$$\frac{952}{2} = {\color{red}476}$$$.

Determine whether $$$476$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$476$$$ by $$${\color{green}2}$$$: $$$\frac{476}{2} = {\color{red}238}$$$.

Determine whether $$$238$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$238$$$ by $$${\color{green}2}$$$: $$$\frac{238}{2} = {\color{red}119}$$$.

Determine whether $$$119$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$119$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$119$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$119$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$119$$$ by $$${\color{green}7}$$$: $$$\frac{119}{7} = {\color{red}17}$$$.

The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.

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: $$$1904 = 2^{4} \cdot 7 \cdot 17$$$.

The prime factorization is $$$1904 = 2^{4} \cdot 7 \cdot 17$$$A.