A prime number is a number that has exactly two distinct positive factors: $1$ and itself. To determine if a number is prime, check whether any whole numbers other than $1$ and the number itself divide into it without leaving a remainder.
In this guide, we’ll check if $37$ is prime using a fast step-by-step method.
What Is A Prime Number?
A prime number has only two factors:
$$ \text{Factors of a prime number} = {1, \text{the number itself}} $$
If any other number divides it evenly, then it is not prime.
Step-by-Step: Is 37 Prime?
We test all integers from $2$ up to $\sqrt{37} \approx 6.08$. We stop once we’ve exceeded the square root.
Try 2:
$$ 37 \div 2 = 18.5 \quad \text{(not a whole number)} $$
Try 3:
$$ 37 \div 3 \approx 12.33 \quad \text{(not a whole number)} $$
Try 4:
$$ 37 \div 4 = 9.25 \quad \text{(not a whole number)} $$
Try 5:
$$ 37 \div 5 = 7.4 \quad \text{(not a whole number)} $$
Try 6:
$$ 37 \div 6 \approx 6.17 \quad \text{(not a whole number)} $$
We’ve now tested all whole numbers up to $\lfloor \sqrt{37} \rfloor = 6$. None divide into $37$ evenly.
✅ Therefore, $37$ has only two factors: $1$ and $37$.
Final Answer
The number $37$ is a prime number.