Prime factorization of $$$2047$$$

Find the prime factorization of $$$2047$$$.

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

Determine whether $$$2047$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2047$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2047$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2047$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$2047$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$2047$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$2047$$$ is divisible by $$$17$$$.

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

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

Determine whether $$$2047$$$ is divisible by $$$19$$$.

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

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

Determine whether $$$2047$$$ is divisible by $$$23$$$.

It is divisible, thus, divide $$$2047$$$ by $$${\color{green}23}$$$: $$$\frac{2047}{23} = {\color{red}89}$$$.

The prime number $$${\color{green}89}$$$ has no other factors then $$$1$$$ and $$${\color{green}89}$$$: $$$\frac{89}{89} = {\color{red}1}$$$.

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: $$$2047 = 23 \cdot 89$$$.

The prime factorization is $$$2047 = 23 \cdot 89$$$A.