How Do You Find the Factors Between Two Numbers?
To find the common factors between two numbers, simply compare the factors of each number. Any number that appears in both lists is a common factor.
For example, the common factors for 32 and 80 are:
1, 2, 4, 8, and 16
Step-by-Step: Get Common Factors of 32 and 80
Step 1: Identify the Smaller Number
Between 32 and 80, the smaller number is 32.
Step 2: Find All the Factors of 32
- Start with 1 and 32 → Add both
- 32 ÷ 2 = 16 → Add 2 and 16
- 32 ÷ 3 = 10.67 → Not a factor
- 32 ÷ 4 = 8 → Add 4 and 8
- 32 ÷ 5 = 6.4 → Not a factor
- Stop here: √32 ≈ 5.6
✅ Factors of 32:
1, 2, 4, 8, 16, 32
Step 3: Check Which of These Also Divide 80
| Factor | Divides 80? | Add to Common Factor List? |
|---|---|---|
| 1 | ✅ Yes | ✅ Yes |
| 2 | ✅ Yes | ✅ Yes |
| 4 | ✅ Yes | ✅ Yes |
| 8 | ✅ Yes | ✅ Yes |
| 16 | ✅ Yes | ✅ Yes |
| 32 | ❌ No | ❌ No |
✅ Common factors of 32 and 80:
1, 2, 4, 8, and 16
Summary
To find common factors between two numbers:
- Begin with the smaller number.
- Find all its factors.
- Check which of those divide evenly into the larger number.
The numbers that divide both without leaving a remainder are your common factors.
For 32 and 80, the common factors are:
1, 2, 4, 8, and 16
Try more examples yourself: