What Is a Prime Number?

A prime number is a whole number greater than 1 that has only two factors:

  • 1
  • Itself

That means the number cannot be evenly divided by any number other than 1 and itself.

Step-by-Step Test for 71

To test if 71 is prime, we divide it by every whole number up to its square root:

$$ \sqrt{71} \approx 8.4 $$

So we test all integers from 2 through 8.

Test for Factors

  • $71 \div 2 = 35.5$ → ❌ not divisible
  • $71 \div 3 \approx 23.67$ → ❌ not divisible
  • $71 \div 4 = 17.75$ → ❌ not divisible
  • $71 \div 5 = 14.2$ → ❌ not divisible
  • $71 \div 6 \approx 11.83$ → ❌ not divisible
  • $71 \div 7 \approx 10.14$ → ❌ not divisible
  • $71 \div 8 \approx 8.875$ → ❌ not divisible

No numbers divide 71 without leaving a remainder.

Final Answer

Since no numbers other than 1 and 71 divide evenly into 71, we conclude:

$$ \boxed{71\ \text{is a prime number.}} $$

Summary

  • A prime number has exactly two factors: 1 and itself.
  • 71 is not divisible by any number between 2 and 8.
  • Therefore, 71 is a prime number.