A prime number is a number that has exactly two positive factors: $1$ and itself. If no other positive integers divide evenly into it, the number is considered prime.
This article explains how to determine if $43$ is prime using a simple step-by-step method.
What Is A Prime Number?
A prime number has exactly two factors:
$$ \text{Factors of a prime number} = {1, \text{the number itself}} $$
If we discover any additional factor, the number is not prime.
Step-by-Step: Is 43 Prime?
We test whether $43$ can be divided evenly by any integer from $2$ up to $\sqrt{43} \approx 6.56$.
Try 2:
$$ 43 \div 2 = 21.5 \quad \text{(not a whole number)} $$
Try 3:
$$ 43 \div 3 \approx 14.33 \quad \text{(not a whole number)} $$
Try 4:
$$ 43 \div 4 = 10.75 \quad \text{(not a whole number)} $$
Try 5:
$$ 43 \div 5 = 8.6 \quad \text{(not a whole number)} $$
Try 6:
$$ 43 \div 6 \approx 7.17 \quad \text{(not a whole number)} $$
Since we have passed all integers up to $\lfloor \sqrt{43} \rfloor = 6$, we can stop here.
✅ No other factors were found, so $43$ has only two positive divisors: $1$ and $43$.
Final Answer
The number $43$ is a prime number.