What Is a Prime Number?

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

  • The number 1
  • The number itself

That means a prime number cannot be evenly divided (i.e., no remainder) by any other number.

How Do You Know If a Number Is Prime?

To determine whether a number is prime:

  1. Start at 2 and test all whole numbers up to the square root of the number.
  2. If none of these divide evenly, the number is prime.
  3. If any do, the number is composite (i.e., not prime).

Let’s use this process to check the number 89.

Is 89 a Prime Number?

We’ll test all whole numbers up to:

$$ \sqrt{89} \approx 9.43 $$

So we check divisibility by 2 through 9.

Divisibility Check:

  • ( 89 \div 2 = 44.5 ) → ❌ remainder
  • ( 89 \div 3 \approx 29.7 ) → ❌ remainder
  • ( 89 \div 4 = 22.25 ) → ❌ remainder
  • ( 89 \div 5 = 17.8 ) → ❌ remainder
  • ( 89 \div 6 \approx 14.8 ) → ❌ remainder
  • ( 89 \div 7 \approx 12.7 ) → ❌ remainder
  • ( 89 \div 8 = 11.125 ) → ❌ remainder
  • ( 89 \div 9 \approx 9.88 ) → ❌ remainder

None of these divide evenly. Therefore:

$$ \boxed{89\ \text{is a prime number.}} $$

Summary

  • A prime number has exactly two factors: 1 and itself.
  • 89 has no divisors other than 1 and 89.
  • So, 89 is a prime number.