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 divided evenly (without a remainder) by any other number.

How To Check if a Number Is Prime

To test whether a number is prime, follow this process:

  1. Try dividing the number by all whole numbers from 2 up to its square root.
  2. If any of those divide evenly, the number is not prime.
  3. If none divide evenly, the number is prime.

Let’s use this method to test the number 91.

Is 91 a Prime Number?

We only need to test divisors up to:

$$ \sqrt{91} \approx 9.5 $$

That means we check 2 through 9.

Step-by-step Test:

  • ( 91 \div 2 = 45.5 ) → ❌ remainder
  • ( 91 \div 3 = 30.33 ) → ❌ remainder
  • ( 91 \div 4 = 22.75 ) → ❌ remainder
  • ( 91 \div 5 = 18.2 ) → ❌ remainder
  • ( 91 \div 6 = 15.17 ) → ❌ remainder
  • ( 91 \div 7 = 13 ) → ✅ no remainder!

So, 91 has these factors:
$$ 1,\ 7,\ 13,\ 91 $$

This means it is not a prime number because it has more than two factors.

Final Answer

Since 91 can be divided evenly by 7:

$$ \boxed{91\ \text{is not a prime number.}} $$

Summary

  • Prime numbers have exactly two factors.
  • 91 has four factors: 1, 7, 13, and 91.
  • Therefore, 91 is not a prime number.