How Can You Quickly Find the Factors of a Number?

Factors are numbers that divide evenly into another number—without leaving a remainder. A factor is never greater than the number itself.

Fast Strategy to Find Factors

  1. Always begin with 1 and the original number.
  2. Incrementally test all integers from 2 up to the square root.
  3. For each number that divides evenly:
    • Add both the number and its quotient.
  4. Stop at the square root (you’ll already have matched pairs).
  5. If you only find two numbers, it’s prime.
  6. If you find more than two, it’s composite.
  7. The highest proper factor is the largest factor excluding the number itself.

Step-by-Step: Find Factors of 60

Follow the process below:

  1. Start with 1 and 60 → list: 1, 60
  2. Try 2 → 60 ÷ 2 = 30 → add 2 and 30 → 1, 2, 30, 60
  3. Try 3 → 60 ÷ 3 = 20 → add 3 and 20 → 1, 2, 3, 20, 30, 60
  4. Try 4 → 60 ÷ 4 = 15 → add 4 and 15 → 1, 2, 3, 4, 15, 20, 30, 60
  5. Try 5 → 60 ÷ 5 = 12 → add 5 and 12 → 1, 2, 3, 4, 5, 12, 15, 20, 30, 60
  6. Try 6 → 60 ÷ 6 = 10 → add 6 and 10 → 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  7. Try 7 → 60 ÷ 7 = 8.57… → not a factor

You’re now past the square root of 60 (≈7.75), so you’re done.

✅ Final list:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

  • It has more than two factors → composite number
  • The highest factor (excluding 60) is 30

Summary

  • Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  • It’s a composite number
  • Highest proper factor is 30

Try it yourself!
Next challenge: Find the factors of 36