A prime number is a number that has exactly two positive factors: $1$ and itself. This guide walks through a step-by-step method to determine if $47$ is a prime number.
What Is A Prime Number?
A number is considered prime if it has only two distinct positive divisors:
$$ \text{Factors of a prime number} = {1, \text{the number itself}} $$
If you can find any other factor, then the number is not prime.
Step-by-Step: Is 47 Prime?
We test whether $47$ can be divided evenly by any integer from $2$ up to $\sqrt{47} \approx 6.86$.
Try 2:
$$ 47 \div 2 = 23.5 \quad \text{(not a whole number)} $$
Try 3:
$$ 47 \div 3 \approx 15.67 \quad \text{(not a whole number)} $$
Try 4:
$$ 47 \div 4 = 11.75 \quad \text{(not a whole number)} $$
Try 5:
$$ 47 \div 5 = 9.4 \quad \text{(not a whole number)} $$
Try 6:
$$ 47 \div 6 \approx 7.83 \quad \text{(not a whole number)} $$
At this point, we’ve reached integers greater than $\sqrt{47}$, so we can stop.
✅ Since none of these numbers divide $47$ evenly, the number has no factors other than $1$ and $47$.
Final Answer
$47$ has only two factors: $1$ and $47$.
✅ So, $47$ is a prime number.