# Prime factorization of $4616$

The calculator will find the prime factorization of $4616$, with steps shown.

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Find the prime factorization of $4616$.

### Solution

Start with the number $2$.

Determine whether $4616$ is divisible by $2$.

It is divisible, thus, divide $4616$ by ${\color{green}2}$: $\frac{4616}{2} = {\color{red}2308}$.

Determine whether $2308$ is divisible by $2$.

It is divisible, thus, divide $2308$ by ${\color{green}2}$: $\frac{2308}{2} = {\color{red}1154}$.

Determine whether $1154$ is divisible by $2$.

It is divisible, thus, divide $1154$ by ${\color{green}2}$: $\frac{1154}{2} = {\color{red}577}$.

The prime number ${\color{green}577}$ has no other factors then $1$ and ${\color{green}577}$: $\frac{577}{577} = {\color{red}1}$.

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: $4616 = 2^{3} \cdot 577$.

The prime factorization is $4616 = 2^{3} \cdot 577$A.