How Can You Quickly Find the Factors of a Number?

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

To find factors efficiently:

  1. Start with the number 1 (it divides into every number).
  2. Then check 2, 3, 4… and so on, up to the square root of the number.
  3. If a number divides evenly into your original number, add it and its quotient to the list.
  4. Stop once your factor exceeds the square root.
  5. If only two numbers (1 and itself) appear, it’s a prime number.
  6. If more than two, it’s a composite number.
  7. To find the highest factor other than itself, look for the next largest in your list.

Find Factors of 42 – Step-by-Step

Let’s work through finding the factors of 42.

  1. Start your factor list: 1 and 42
  2. Try 2: 42 ÷ 2 = 21 → add 2 and 21
  3. Try 3: 42 ÷ 3 = 14 → add 3 and 14
  4. Try 4: 42 ÷ 4 = 10.5 → not a factor
  5. Try 5: 42 ÷ 5 = 8.4 → not a factor
  6. Try 6: 42 ÷ 6 = 7 → add 6 and 7
  7. You’ve reached the square root of 42 (≈6.5), so stop here.

✅ Final list of factors:
1, 2, 3, 6, 7, 14, 21, 42

Since there are more than 2 factors, 42 is a composite number.

📌 The highest factor other than 42 is 21.

Summary

  • Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
  • It’s a composite number because it has more than two factors.
  • The highest proper factor of 42 is 21.

Now try using the same process to find the
👉 factors of 60