# Prime factorization of $2563$

The calculator will find the prime factorization of $2563$, with steps shown.

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Find the prime factorization of $2563$.

### Solution

Start with the number $2$.

Determine whether $2563$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2563$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2563$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $2563$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $2563$ is divisible by $11$.

It is divisible, thus, divide $2563$ by ${\color{green}11}$: $\frac{2563}{11} = {\color{red}233}$.

The prime number ${\color{green}233}$ has no other factors then $1$ and ${\color{green}233}$: $\frac{233}{233} = {\color{red}1}$.

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: $2563 = 11 \cdot 233$.

The prime factorization is $2563 = 11 \cdot 233$A.