Prime factorization of $$$4656$$$

Find the prime factorization of $$$4656$$$.

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.