# Prime factorization of $1904$

The calculator will find the prime factorization of $1904$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $1904$.

### Solution

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.