What Is a Prime Number?

A prime number is a number that has exactly two factors:

  • (1)
  • itself

If a number has more than two factors, it is called a composite number.

Step-by-Step Check: Is 43 Prime?

Let’s test whether (43) is prime by checking if it has any divisors other than 1 and itself. We only need to test numbers up to (\sqrt{43} \approx 6.56).

Try dividing by small primes:

  • (43 \div 2 = 21.5) → ✖️ Not divisible
  • (43 \div 3 \approx 14.33) → ✖️ Not divisible
  • (43 \div 4 = 10.75) → ✖️ Not divisible
  • (43 \div 5 = 8.6) → ✖️ Not divisible
  • (43 \div 6 \approx 7.17) → ✖️ Not divisible

Since no divisors were found up to (\sqrt{43}), we can conclude:

[ \boxed{43\ \text{is a prime number.}} ]

Summary

  • A prime number has only two factors: (1) and itself.
  • (43) has no divisors other than (1) and (43).
  • ✅ Therefore, 43 is a prime number.