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 called a composite number.

Is 59 a Prime Number?

To determine if 59 is a prime number, test whether any number between 2 and ( \sqrt{59} \approx 7.68 ) divides evenly into 59.

We only need to check integers up to 7.

Trial Division Steps

  • (59 \div 2 = 29.5) → ❌ Not divisible
  • (59 \div 3 \approx 19.67) → ❌ Not divisible
  • (59 \div 4 = 14.75) → ❌ Not divisible
  • (59 \div 5 = 11.8) → ❌ Not divisible
  • (59 \div 6 \approx 9.83) → ❌ Not divisible
  • (59 \div 7 \approx 8.43) → ❌ Not divisible

None divide evenly. Since no divisors other than 1 and 59 exist, 59 is a prime number.

Conclusion

$$ \boxed{59\ \text{is a prime number.}} $$

Because no number other than 1 and 59 divides 59 exactly, it meets the criteria for being a prime number.

Summary

  • Prime numbers have only two factors: 1 and the number itself.
  • 59 is not divisible by any integer between 2 and 7.
  • ✅ 59 is a prime number.