Find GCF/HCF and all common factors of two or more numbers.
Common Factors — How to Find Them
Common factors of two or more numbers are factors that all the numbers share. The largest of these common factors is the GCF (Greatest Common Factor). Finding common factors is useful for simplifying fractions, solving ratio problems, and distributing items equally.
| Numbers | Factors of Each | Common Factors | GCF |
|---|
| 12, 18 | 12: 1,2,3,4,6,12 | 18: 1,2,3,6,9,18 | 1, 2, 3, 6 | 6 |
| 20, 30 | 20: 1,2,4,5,10,20 | 30: 1,2,3,5,6,10,15,30 | 1, 2, 5, 10 | 10 |
| 7, 11 | 7: 1,7 | 11: 1,11 | 1 only | 1 (co-prime) |
| 24, 36, 48 | Multiple sets | 1,2,3,4,6,12 | 12 |
What does it mean when two numbers have GCF of 1?
When GCF=1, the numbers are called co-prime or relatively prime — they share no common factors except 1. Example: 7 and 13 are co-prime. Co-prime numbers don't have to be prime themselves — 8 and 15 are co-prime (GCF=1) even though neither is prime.
How are common factors used in real life?
Common factors help you divide items into equal groups without leftovers. Example: You have 24 apples and 36 oranges, want to make identical gift baskets using all items. GCF(24,36)=12 → you can make 12 baskets with 2 apples and 3 oranges each.
Calculatr