What Is a Prime Number?

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

  • (1)
  • itself

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

Step-by-Step Test: Is 39 Prime?

We will determine whether (39) is a prime number by testing whether any integers divide evenly into it — without leaving a remainder.

We only need to check up to (\sqrt{39} \approx 6.24).

Try dividing 39 by numbers greater than 1 and less than or equal to 6:

  • (39 \div 2 = 19.5) → ✖️ Not divisible
  • (39 \div 3 = 13) → ✅ Divisible

Since (3 \times 13 = 39), 39 has at least three factors: (1), (3), and (13).

[ \boxed{39\ \text{is not a prime number.}} ]

Summary

  • A prime number has only two factors: (1) and itself.
  • (39) is divisible by (3), so it has more than two factors.
  • ❌ Therefore, 39 is not a prime number.