Prime factorization of $$$4209$$$

Find the prime factorization of $$$4209$$$.

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

Determine whether $$$4209$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4209$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4209$$$ by $$${\color{green}3}$$$: $$$\frac{4209}{3} = {\color{red}1403}$$$.

Determine whether $$$1403$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1403$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1403$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1403$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1403$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$1403$$$ is divisible by $$$17$$$.

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

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

Determine whether $$$1403$$$ is divisible by $$$19$$$.

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

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

Determine whether $$$1403$$$ is divisible by $$$23$$$.

It is divisible, thus, divide $$$1403$$$ by $$${\color{green}23}$$$: $$$\frac{1403}{23} = {\color{red}61}$$$.

The prime number $$${\color{green}61}$$$ has no other factors then $$$1$$$ and $$${\color{green}61}$$$: $$$\frac{61}{61} = {\color{red}1}$$$.

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: $$$4209 = 3 \cdot 23 \cdot 61$$$.

The prime factorization is $$$4209 = 3 \cdot 23 \cdot 61$$$A.