# Prime factorization of $4104$

The calculator will find the prime factorization of $4104$, with steps shown.

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Find the prime factorization of $4104$.

### Solution

Start with the number $2$.

Determine whether $4104$ is divisible by $2$.

It is divisible, thus, divide $4104$ by ${\color{green}2}$: $\frac{4104}{2} = {\color{red}2052}$.

Determine whether $2052$ is divisible by $2$.

It is divisible, thus, divide $2052$ by ${\color{green}2}$: $\frac{2052}{2} = {\color{red}1026}$.

Determine whether $1026$ is divisible by $2$.

It is divisible, thus, divide $1026$ by ${\color{green}2}$: $\frac{1026}{2} = {\color{red}513}$.

Determine whether $513$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $513$ is divisible by $3$.

It is divisible, thus, divide $513$ by ${\color{green}3}$: $\frac{513}{3} = {\color{red}171}$.

Determine whether $171$ is divisible by $3$.

It is divisible, thus, divide $171$ by ${\color{green}3}$: $\frac{171}{3} = {\color{red}57}$.

Determine whether $57$ is divisible by $3$.

It is divisible, thus, divide $57$ by ${\color{green}3}$: $\frac{57}{3} = {\color{red}19}$.

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: $4104 = 2^{3} \cdot 3^{3} \cdot 19$.

The prime factorization is $4104 = 2^{3} \cdot 3^{3} \cdot 19$A.