Prime factorization of $$$4161$$$

Find the prime factorization of $$$4161$$$.

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

Determine whether $$$4161$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4161$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4161$$$ by $$${\color{green}3}$$$: $$$\frac{4161}{3} = {\color{red}1387}$$$.

Determine whether $$$1387$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1387$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1387$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1387$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1387$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$1387$$$ is divisible by $$$17$$$.

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

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

Determine whether $$$1387$$$ is divisible by $$$19$$$.

It is divisible, thus, divide $$$1387$$$ by $$${\color{green}19}$$$: $$$\frac{1387}{19} = {\color{red}73}$$$.

The prime number $$${\color{green}73}$$$ has no other factors then $$$1$$$ and $$${\color{green}73}$$$: $$$\frac{73}{73} = {\color{red}1}$$$.

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: $$$4161 = 3 \cdot 19 \cdot 73$$$.

The prime factorization is $$$4161 = 3 \cdot 19 \cdot 73$$$A.