# Prime factorization of $2047$

The calculator will find the prime factorization of $2047$, with steps shown.

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Find the prime factorization of $2047$.

### Solution

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.