Is 23 A Prime Number? Step By Step Method To Find Out

A prime number is a whole number greater than $1$ that has exactly two distinct factors: $1$ and itself.

To check whether a number is prime, try dividing it by all whole numbers between $2$ and $\sqrt{n}$. If none divide exactly, the number is prime.

What Is A Prime Number?

A number $n$ is prime if:

$$ \text{Factors of } n = {1, n} $$

There should be no other whole number (except $1$ and $n$) that divides it evenly.

Step-by-Step: Is 23 Prime?

We test whole numbers from $2$ to $\lfloor \sqrt{23} \rfloor = 4$.

Try 2:

$$ 23 \div 2 = 11.5 \quad \text{(not a whole number)} $$

Try 3:

$$ 23 \div 3 \approx 7.67 \quad \text{(not a whole number)} $$

Try 4:

$$ 23 \div 4 = 5.75 \quad \text{(not a whole number)} $$

We have tested all whole numbers up to $\sqrt{23}$ and found no divisors.

✅ Therefore, $23$ has only two factors: $1$ and $23$.

Final Answer

The number $23$ is a prime number.