# Prime factorization of $3864$

The calculator will find the prime factorization of $3864$, with steps shown.

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Find the prime factorization of $3864$.

### Solution

Start with the number $2$.

Determine whether $3864$ is divisible by $2$.

It is divisible, thus, divide $3864$ by ${\color{green}2}$: $\frac{3864}{2} = {\color{red}1932}$.

Determine whether $1932$ is divisible by $2$.

It is divisible, thus, divide $1932$ by ${\color{green}2}$: $\frac{1932}{2} = {\color{red}966}$.

Determine whether $966$ is divisible by $2$.

It is divisible, thus, divide $966$ by ${\color{green}2}$: $\frac{966}{2} = {\color{red}483}$.

Determine whether $483$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $483$ is divisible by $3$.

It is divisible, thus, divide $483$ by ${\color{green}3}$: $\frac{483}{3} = {\color{red}161}$.

Determine whether $161$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $161$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $161$ is divisible by $7$.

It is divisible, thus, divide $161$ by ${\color{green}7}$: $\frac{161}{7} = {\color{red}23}$.

The prime number ${\color{green}23}$ has no other factors then $1$ and ${\color{green}23}$: $\frac{23}{23} = {\color{red}1}$.

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: $3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23$.

The prime factorization is $3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23$A.