# Prime factorization of $1896$

The calculator will find the prime factorization of $1896$, with steps shown.

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Find the prime factorization of $1896$.

### Solution

Start with the number $2$.

Determine whether $1896$ is divisible by $2$.

It is divisible, thus, divide $1896$ by ${\color{green}2}$: $\frac{1896}{2} = {\color{red}948}$.

Determine whether $948$ is divisible by $2$.

It is divisible, thus, divide $948$ by ${\color{green}2}$: $\frac{948}{2} = {\color{red}474}$.

Determine whether $474$ is divisible by $2$.

It is divisible, thus, divide $474$ by ${\color{green}2}$: $\frac{474}{2} = {\color{red}237}$.

Determine whether $237$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $237$ is divisible by $3$.

It is divisible, thus, divide $237$ by ${\color{green}3}$: $\frac{237}{3} = {\color{red}79}$.

The prime number ${\color{green}79}$ has no other factors then $1$ and ${\color{green}79}$: $\frac{79}{79} = {\color{red}1}$.

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: $1896 = 2^{3} \cdot 3 \cdot 79$.

The prime factorization is $1896 = 2^{3} \cdot 3 \cdot 79$A.