How To Tell If 13 Is A Prime Number Or Not

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

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

What Is A Prime Number?

A number $n$ is prime if:

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

It cannot be evenly divided by any number other than $1$ and itself.

Step-by-Step: Is 13 Prime?

We test integers from $2$ up to $\lfloor \sqrt{13} \rfloor = 3$.

Try 2:

$$ 13 \div 2 = 6.5 \quad \text{(not a whole number)} $$

Try 3:

$$ 13 \div 3 \approx 4.33 \quad \text{(not a whole number)} $$

We have tested all divisors up to $\sqrt{13}$ and found no exact divisors.

✅ Therefore, $13$ has only two factors: $1$ and $13$.

Final Answer

The number $13$ is a prime number.