How Can You Quickly Find the Factors of a Number?

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

To find factors quickly:

  1. Always include 1 and the original number.
  2. Start testing from 2 up to the square root of the number.
  3. If a number divides evenly, add both it and its quotient.
  4. Stop once you reach the square root.
  5. If only two numbers are found, the number is prime.
  6. If more than two, it’s composite.
  7. To find the highest proper factor (excluding the number itself), look at the next largest number in your list.

Find Factors of 48 – Step-by-Step

Let’s find the factors of 48 by checking every number up to its square root.

  1. Begin with 1 and 48
  2. Try 2: 48 ÷ 2 = 24 → add 2 and 24
  3. Try 3: 48 ÷ 3 = 16 → add 3 and 16
  4. Try 4: 48 ÷ 4 = 12 → add 4 and 12
  5. Try 5: 48 ÷ 5 = 9.6 → not a factor
  6. Try 6: 48 ÷ 6 = 8 → add 6 and 8
  7. You’ve reached the square root of 48 (≈6.9), so stop here.

✅ Final list of factors:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Since it has more than two factors, 48 is a composite number.

📌 The highest factor other than 48 is 24.

Summary

  • Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  • It’s a composite number
  • The highest proper factor is 24

Next challenge: Try applying the same steps to find the
👉 factors of 42