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 classified as composite.

Step-by-Step: Is 49 Prime?

Let’s determine whether (49) is a prime number by checking its divisibility by integers greater than 1 and less than or equal to (\sqrt{49} = 7).

Check small divisors:

  • (49 \div 2 = 24.5) → ✖️ Not divisible
  • (49 \div 3 \approx 16.33) → ✖️ Not divisible
  • (49 \div 4 = 12.25) → ✖️ Not divisible
  • (49 \div 5 = 9.8) → ✖️ Not divisible
  • (49 \div 6 \approx 8.17) → ✖️ Not divisible
  • (49 \div 7 = 7) → ✔️ Divisible

Since (7 \times 7 = 49), this means (49) has an additional factor other than (1) and itself.

Conclusion

Because (49) is divisible by (7), it has three factors: (1), (7), and (49).

[ \boxed{49\ \text{is not a prime number.}} ]

Summary

  • A prime number has exactly two factors.
  • (49) has more than two factors: (1, 7, 49).
  • Therefore, 49 is not a prime number.