How can you quickly find the factors of a number?

Factors are numbers that divide evenly into another number — with no remainder. A factor can never be greater than the number itself.

To find factors quickly:

  1. Start with 1 and the number itself — these are always factors.
  2. Begin checking each number from 2 upwards:
    • Ask: Does this number divide into the original without remainder?
    • If yes, add both the divisor and the quotient.
  3. Stop when your checking number exceeds the square root of the original number.

If the result has only two factors, it’s prime.
If it has more than two, it’s composite.

Let’s apply this to the number 80.

Find Factors Of 80

Step-by-step:

  • Start with: $[1, 80]$
  • Try 2: $80 \div 2 = 40$ → ✅ → add 2 and 40
  • Try 3: $80 \div 3 = 26.66\ldots$ → ❌
  • Try 4: $80 \div 4 = 20$ → ✅ → add 4 and 20
  • Try 5: $80 \div 5 = 16$ → ✅ → add 5 and 16
  • Try 6: $80 \div 6 = 13.33\ldots$ → ❌
  • Try 7: $80 \div 7 = 11.43\ldots$ → ❌
  • Try 8: $80 \div 8 = 10$ → ✅ → add 8 and 10

You’ve now reached $\sqrt{80} \approx 8.94$, so you can stop.

Final factor list:

$$ [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] $$

  • Since 80 has more than two factors, it is a composite number.
  • The highest factor other than 80 is 40.

Summary

The factors of 80 are:

$$ [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] $$

  • If a number only has 1 and itself as factors, it is a prime number.
  • If it has more than 2 factors, it is a composite number.

Since 80 has many divisors, it is clearly composite.