What Is a Prime Number?

A prime number is a number with exactly two factors:

  • The number 1
  • The number itself

That means a prime number cannot be divided evenly by any other whole number.

How Can You Check If a Number Is Prime?

To test whether a number is prime:

  1. Begin dividing by small numbers, starting at 2.
  2. Stop once you’ve reached the square root of the number.
  3. If no divisor leaves a remainder of 0 (besides 1 and the number itself), it is prime.

Let’s test this using 73.

Step-by-Step Test for 73

The square root of 73 is approximately:

$$ \sqrt{73} \approx 8.54 $$

So we test divisibility from 2 through 8.

Divisibility Test:

  • ( 73 \div 2 = 36.5 ) → ❌ remainder
  • ( 73 \div 3 \approx 24.33 ) → ❌ remainder
  • ( 73 \div 4 = 18.25 ) → ❌ remainder
  • ( 73 \div 5 = 14.6 ) → ❌ remainder
  • ( 73 \div 6 \approx 12.17 ) → ❌ remainder
  • ( 73 \div 7 \approx 10.43 ) → ❌ remainder
  • ( 73 \div 8 \approx 9.125 ) → ❌ remainder

There are no whole number factors between 2 and 8.

Conclusion

Since only 1 and 73 divide 73 without a remainder:

$$ \boxed{73\ \text{is a prime number.}} $$

Summary

  • A prime number has only two factors: 1 and itself.
  • 73 has no other divisors.
  • So, 73 is a prime number.