What Is a Prime Number?

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

  • (1)
  • The number itself

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

Step-by-Step Test for 63

We’ll check if any number from 2 up to ( \sqrt{63} \approx 7.94 ) divides 63 evenly:

Try Dividing 63 By:

  • (63 \div 2 = 31.5) → ❌ Not divisible
  • (63 \div 3 = 21) → ✅ Divisible
  • No need to check further. We’ve found another factor!

Conclusion

Since 63 has more than two factors — (1), (3), (21), and (63) — it is not a prime number.

$$ \boxed{63\ \text{is not a prime number.}} $$

Summary

  • A prime number has exactly two factors: (1) and itself.
  • (63) is divisible by (3), so it has more than two factors.
  • Therefore, 63 is a composite number, not a prime.