Prime factorization of $$$4646$$$

Find the prime factorization of $$$4646$$$.

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

Determine whether $$$4646$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4646$$$ by $$${\color{green}2}$$$: $$$\frac{4646}{2} = {\color{red}2323}$$$.

Determine whether $$$2323$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2323$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2323$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$2323$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$2323$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$2323$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$2323$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$2323$$$ is divisible by $$$19$$$.

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

The next prime number is $$$23$$$.

Determine whether $$$2323$$$ is divisible by $$$23$$$.

It is divisible, thus, divide $$$2323$$$ by $$${\color{green}23}$$$: $$$\frac{2323}{23} = {\color{red}101}$$$.

The prime number $$${\color{green}101}$$$ has no other factors then $$$1$$$ and $$${\color{green}101}$$$: $$$\frac{101}{101} = {\color{red}1}$$$.

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: $$$4646 = 2 \cdot 23 \cdot 101$$$.

The prime factorization is $$$4646 = 2 \cdot 23 \cdot 101$$$A.