Prime factorization of $$$4660$$$

Find the prime factorization of $$$4660$$$.

Start with the number $$$2$$$.

Determine whether $$$4660$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4660$$$ by $$${\color{green}2}$$$: $$$\frac{4660}{2} = {\color{red}2330}$$$.

Determine whether $$$2330$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2330$$$ by $$${\color{green}2}$$$: $$$\frac{2330}{2} = {\color{red}1165}$$$.

Determine whether $$$1165$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$1165$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$1165$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1165$$$ by $$${\color{green}5}$$$: $$$\frac{1165}{5} = {\color{red}233}$$$.

The prime number $$${\color{green}233}$$$ has no other factors then $$$1$$$ and $$${\color{green}233}$$$: $$$\frac{233}{233} = {\color{red}1}$$$.

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: $$$4660 = 2^{2} \cdot 5 \cdot 233$$$.

The prime factorization is $$$4660 = 2^{2} \cdot 5 \cdot 233$$$A.