Prime factorization of $$$4186$$$

Find the prime factorization of $$$4186$$$.

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

Determine whether $$$4186$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4186$$$ by $$${\color{green}2}$$$: $$$\frac{4186}{2} = {\color{red}2093}$$$.

Determine whether $$$2093$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2093$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2093$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2093$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$2093$$$ by $$${\color{green}7}$$$: $$$\frac{2093}{7} = {\color{red}299}$$$.

Determine whether $$$299$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$299$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$299$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$299$$$ by $$${\color{green}13}$$$: $$$\frac{299}{13} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$4186 = 2 \cdot 7 \cdot 13 \cdot 23$$$.

The prime factorization is $$$4186 = 2 \cdot 7 \cdot 13 \cdot 23$$$A.