Prime factorization of $$$4686$$$

Find the prime factorization of $$$4686$$$.

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

Determine whether $$$4686$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4686$$$ by $$${\color{green}2}$$$: $$$\frac{4686}{2} = {\color{red}2343}$$$.

Determine whether $$$2343$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2343$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2343$$$ by $$${\color{green}3}$$$: $$$\frac{2343}{3} = {\color{red}781}$$$.

Determine whether $$$781$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$781$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$781$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$781$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$781$$$ by $$${\color{green}11}$$$: $$$\frac{781}{11} = {\color{red}71}$$$.

The prime number $$${\color{green}71}$$$ has no other factors then $$$1$$$ and $$${\color{green}71}$$$: $$$\frac{71}{71} = {\color{red}1}$$$.

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: $$$4686 = 2 \cdot 3 \cdot 11 \cdot 71$$$.

The prime factorization is $$$4686 = 2 \cdot 3 \cdot 11 \cdot 71$$$A.