Common Factor Calculator

Find all common factors shared by two or more numbers. Shows factor lists and intersection.

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Numbers (2–5, comma-separated)

Common Factors

Enter numbers to find common factors

GCF (largest)

LCM

Smallest Common

Simplified Ratio

All Common Factors

Number	All Factors

Find every factor shared by two to five numbers at once, along with their greatest common factor (GCF), least common multiple (LCM), and simplified ratio.

How It Works

How Common Factor Calculator Works

For each number entered, the calculator lists every factor by testing divisors up to its square root and pairing each divisor i with its complement (number ÷ i) — a fast way to generate the complete factor list without checking every integer individually.

It then intersects the factor lists of all entered numbers to find the common factors — the values that appear in every single list. The largest of these common factors is the greatest common factor (GCF), found using the Euclidean algorithm applied across all numbers at once.

The least common multiple (LCM) is computed pairwise using LCM(a,b) = |a × b| ÷ GCD(a,b), reduced across the whole list. The simplified ratio divides every entered number by the GCF, showing the smallest whole-number ratio between them.

Worked Example

See It In Action

For 12, 18, and 24: the factors of 12 are 1,2,3,4,6,12; of 18 are 1,2,3,6,9,18; and of 24 are 1,2,3,4,6,8,12,24. The factors common to all three are 1, 2, 3, and 6 — four common factors in total. The greatest of these, the GCF, is 6; the LCM is 72; and dividing each number by 6 gives the simplified ratio 2 : 3 : 4.

Real-World Use Cases

Who Uses Common Factor Calculator and Why

Simplifying a ratio between three or more quantities — like ingredient amounts in a recipe — down to its smallest whole-number form.
Comparing up to five numbers at once to see every factor they all share, not just the single greatest one.
Verifying a GCF and LCM computed by hand for a small group of related numbers, since both are derived from the same shared factor list.
Splitting several different-sized batches into the largest common group size that divides all of them evenly.

Common Mistakes

Mistakes to Avoid

Expecting to enter more than five numbers — this tool intentionally caps input at 2–5 numbers to keep the shared factor list and intersection readable.
Treating the full list of common factors as the same thing as just the GCF — the GCF is only the largest value in that shared list, and the other common factors are also valid, just smaller.
Assuming the LCM shown alongside the GCF is unrelated — it's computed from the same set of numbers using LCM(a,b) = |a×b| ÷ GCD(a,b), reduced pairwise across the whole list.

Pro Tips

Tips for Best Results

Use the "Simplified Ratio" result directly when scaling a recipe or proportion — it's exactly the numbers divided by their GCF.
If your numbers only share the factor 1, that's a valid coprime result, not a sign of an input error.

Troubleshooting

Fixing Common Problems

I need common factors for more than five numbers. — Split your numbers into groups of five or fewer, find the common factors of each group, then compare those results by hand or feed the group results back through as a smaller set.

The only common factor listed is 1. — That means the numbers are coprime — they genuinely share no factor larger than 1, even though each number individually may have many other factors.

Glossary

Terms Explained

Common factor: A number that divides evenly into every number in a given set.

Simplified ratio: Each number in the set divided by their shared GCF, giving the smallest whole-number relationship between them.

FAQ

Frequently Asked Questions

What's the difference between GCF and LCM?

The GCF (greatest common factor) is the largest number that divides evenly into every entered number, while the LCM (least common multiple) is the smallest number that all of them divide into evenly — GCF shrinks toward the numbers, LCM grows past them.

Why is input limited to 2–5 numbers?

Comparing common factors across more than a handful of numbers quickly becomes hard to read; five numbers keeps the factor lists and the intersection manageable while still covering the vast majority of real use cases.

Can I use this to simplify a ratio or fraction?

Yes — dividing each of your numbers by their GCF (shown as the "Simplified Ratio" result) is exactly how you reduce a ratio or fraction to its lowest terms.

What if the numbers only share the factor 1?

That means the numbers are coprime (relatively prime) — their GCF is 1, and the only "common factor" between them is 1 itself, even though each number may have many factors of its own.