# Prime factorization of $768$

The calculator will find the prime factorization of $768$, with steps shown.

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Find the prime factorization of $768$.

### Solution

Start with the number $2$.

Determine whether $768$ is divisible by $2$.

It is divisible, thus, divide $768$ by ${\color{green}2}$: $\frac{768}{2} = {\color{red}384}$.

Determine whether $384$ is divisible by $2$.

It is divisible, thus, divide $384$ by ${\color{green}2}$: $\frac{384}{2} = {\color{red}192}$.

Determine whether $192$ is divisible by $2$.

It is divisible, thus, divide $192$ by ${\color{green}2}$: $\frac{192}{2} = {\color{red}96}$.

Determine whether $96$ is divisible by $2$.

It is divisible, thus, divide $96$ by ${\color{green}2}$: $\frac{96}{2} = {\color{red}48}$.

Determine whether $48$ is divisible by $2$.

It is divisible, thus, divide $48$ by ${\color{green}2}$: $\frac{48}{2} = {\color{red}24}$.

Determine whether $24$ is divisible by $2$.

It is divisible, thus, divide $24$ by ${\color{green}2}$: $\frac{24}{2} = {\color{red}12}$.

Determine whether $12$ is divisible by $2$.

It is divisible, thus, divide $12$ by ${\color{green}2}$: $\frac{12}{2} = {\color{red}6}$.

Determine whether $6$ is divisible by $2$.

It is divisible, thus, divide $6$ by ${\color{green}2}$: $\frac{6}{2} = {\color{red}3}$.

The prime number ${\color{green}3}$ has no other factors then $1$ and ${\color{green}3}$: $\frac{3}{3} = {\color{red}1}$.

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: $768 = 2^{8} \cdot 3$.

The prime factorization is $768 = 2^{8} \cdot 3$A.