What Is a Prime Number?

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

  1. The number 1
  2. The number itself

That means a prime number cannot be divided evenly (without a remainder) by any other whole number.

How Do You Know If a Number Is Prime?

To check if a number is prime:

  • Start with the number 2.
  • Keep dividing the number by each successive whole number.
  • Stop once the number you’re testing reaches or exceeds the square root of the original number.
  • If no exact division occurs (other than 1 and itself), it’s prime.

Is 97 a Prime Number?

Let’s test:

We want to check if 97 is divisible by any whole number other than 1 or 97.

We only need to test up to the square root of 97.
Since:

$$ \sqrt{97} \approx 9.8 $$

We test integers up to 9.

Test Each Whole Number:

  • ( 97 \div 2 = 48.5 ) → ❌ remainder
  • ( 97 \div 3 = 32.3 ) → ❌ remainder
  • ( 97 \div 4 = 24.25 ) → ❌ remainder
  • ( 97 \div 5 = 19.4 ) → ❌ remainder
  • ( 97 \div 6 = 16.17 ) → ❌ remainder
  • ( 97 \div 7 = 13.86 ) → ❌ remainder
  • ( 97 \div 8 = 12.125 ) → ❌ remainder
  • ( 97 \div 9 = 10.78 ) → ❌ remainder

✅ None divide evenly into 97.

Final Answer

Since only 1 and 97 divide evenly into 97:

$$ \text{Factors of 97} = {1,\ 97} $$

That means:

$$ \boxed{97\ \text{is a prime number.}} $$

Is 97 the Largest 2-Digit Prime?

Yes!

  • 98 is even → divisible by 2.
  • 99 is divisible by 3 and 11.
  • 100 is divisible by 2 and 5.

✅ So, 97 is the largest 2-digit prime number.

Summary

  • Prime numbers have exactly two factors: 1 and itself.
  • The number 97 cannot be divided evenly by any number other than 1 and 97.
  • Therefore, 97 is a prime number.
  • It is also the largest 2-digit prime.