# Prime factorization of $4864$

The calculator will find the prime factorization of $4864$, with steps shown.

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Find the prime factorization of $4864$.

### Solution

Start with the number $2$.

Determine whether $4864$ is divisible by $2$.

It is divisible, thus, divide $4864$ by ${\color{green}2}$: $\frac{4864}{2} = {\color{red}2432}$.

Determine whether $2432$ is divisible by $2$.

It is divisible, thus, divide $2432$ by ${\color{green}2}$: $\frac{2432}{2} = {\color{red}1216}$.

Determine whether $1216$ is divisible by $2$.

It is divisible, thus, divide $1216$ by ${\color{green}2}$: $\frac{1216}{2} = {\color{red}608}$.

Determine whether $608$ is divisible by $2$.

It is divisible, thus, divide $608$ by ${\color{green}2}$: $\frac{608}{2} = {\color{red}304}$.

Determine whether $304$ is divisible by $2$.

It is divisible, thus, divide $304$ by ${\color{green}2}$: $\frac{304}{2} = {\color{red}152}$.

Determine whether $152$ is divisible by $2$.

It is divisible, thus, divide $152$ by ${\color{green}2}$: $\frac{152}{2} = {\color{red}76}$.

Determine whether $76$ is divisible by $2$.

It is divisible, thus, divide $76$ by ${\color{green}2}$: $\frac{76}{2} = {\color{red}38}$.

Determine whether $38$ is divisible by $2$.

It is divisible, thus, divide $38$ by ${\color{green}2}$: $\frac{38}{2} = {\color{red}19}$.

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: $4864 = 2^{8} \cdot 19$.

The prime factorization is $4864 = 2^{8} \cdot 19$A.