How Do You Find the Factors Between Two Numbers — Quickly?

To find the common factors between two numbers, compare the list of factors for each number. Any number that appears in both lists is known as a common factor.

For example, the common factors of 28 and 42 are:

1, 2, 7, and 14

Step-by-Step: Get Common Factors of 28 and 42

Step 1: Identify the smaller number

Between 28 and 42, the smaller number is 28.

Step 2: Find all the factors of 28

  • Start with 1 and 28 → Add both
  • 28 ÷ 2 = 14 → Add 2 and 14
  • 28 ÷ 3 = 9.33 → Not a factor
  • 28 ÷ 4 = 7 → Add 4 and 7
  • 28 ÷ 5 = 5.6 → Not a factor
  • Stop at √28 ≈ 5.2

✅ Final factors of 28:
1, 2, 4, 7, 14, 28

Step 3: Check which of these also divide into 42

FactorDivides 42?Common Factor?
1✅ Yes✅ Yes
2✅ Yes✅ Yes
4❌ No❌ No
7✅ Yes✅ Yes
14✅ Yes✅ Yes
28❌ No❌ No

✅ Final list of common factors:
1, 2, 7, 14

Summary

To find the common factors of two numbers:

  1. Start with the smaller number.
  2. List all its factors.
  3. Check which of those divide into the larger number.
  4. The numbers that divide both without remainder are the common factors.

For 28 and 42, the common factors are:
1, 2, 7, and 14

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