# Prime factorization of $4656$

The calculator will find the prime factorization of $4656$, with steps shown.

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Find the prime factorization of $4656$.

### Solution

Start with the number $2$.

Determine whether $4656$ is divisible by $2$.

It is divisible, thus, divide $4656$ by ${\color{green}2}$: $\frac{4656}{2} = {\color{red}2328}$.

Determine whether $2328$ is divisible by $2$.

It is divisible, thus, divide $2328$ by ${\color{green}2}$: $\frac{2328}{2} = {\color{red}1164}$.

Determine whether $1164$ is divisible by $2$.

It is divisible, thus, divide $1164$ by ${\color{green}2}$: $\frac{1164}{2} = {\color{red}582}$.

Determine whether $582$ is divisible by $2$.

It is divisible, thus, divide $582$ by ${\color{green}2}$: $\frac{582}{2} = {\color{red}291}$.

Determine whether $291$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $291$ is divisible by $3$.

It is divisible, thus, divide $291$ by ${\color{green}3}$: $\frac{291}{3} = {\color{red}97}$.

The prime number ${\color{green}97}$ has no other factors then $1$ and ${\color{green}97}$: $\frac{97}{97} = {\color{red}1}$.

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: $4656 = 2^{4} \cdot 3 \cdot 97$.

The prime factorization is $4656 = 2^{4} \cdot 3 \cdot 97$A.