How Can You Quickly Find the Factors of a Number?

Factors are numbers that divide exactly into another number without leaving a remainder. A factor is always less than or equal to the number itself.

Quick Steps to Find Factors

  1. Always begin with 1 and the number itself.
  2. Try dividing by each integer starting from 2 up to the square root.
  3. If a number divides evenly, add it and its quotient to the list.
  4. Stop when your divisor exceeds the square root.
  5. If you only have two factors, it’s a prime number.
  6. More than two factors? It’s a composite number.
  7. The largest factor (excluding the number itself) is the highest proper factor.

Step-by-Step: Find Factors of 4

Follow the process below:

  1. Start with 1 and 4 → 1, 4
  2. Try 2 → 4 ÷ 2 = 2
    • 2 × 2 = 4 → only add 2 once
    • Updated list: 1, 2, 4
  3. You’ve now reached the square root of 4 (√4 = 2), so stop here.

✅ Final list of factors: 1, 2, 4

  • More than 2 factors → composite number
  • Highest proper factor: 2

Summary

  • Factors of 4: 1, 2, 4
  • Classification: Composite number
  • Highest factor (excluding 4): 2

Want a new challenge? Try your hand at finding the factors of 6 or the factors of 9.