What Is a Prime Number?

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

  • (1)
  • Itself

This means no other whole number can divide into it evenly.

How To Check If 67 Is Prime

To determine if 67 is a prime number, we check for factors other than 1 and 67 by dividing it by all integers up to its square root:

$$ \sqrt{67} \approx 8.19 $$

So we test numbers from 2 to 8.

Step-by-Step Factor Check

  • (67 \div 2 = 33.5) → ❌ Not divisible
  • (67 \div 3 \approx 22.33) → ❌ Not divisible
  • (67 \div 4 = 16.75) → ❌ Not divisible
  • (67 \div 5 = 13.4) → ❌ Not divisible
  • (67 \div 6 \approx 11.17) → ❌ Not divisible
  • (67 \div 7 \approx 9.57) → ❌ Not divisible
  • (67 \div 8 \approx 8.375) → ❌ Not divisible

Final Answer

Since none of the integers from 2 to 8 divide 67 without a remainder:

$$ \boxed{67\ \text{is a prime number.}} $$

Summary

  • A prime number has exactly two factors: 1 and itself.
  • 67 cannot be divided evenly by any number other than 1 and 67.
  • Therefore, 67 is a prime number.