Common Factor Calculator
Common Factors1, 2, 3, 6
GCF6
The common factor calculator compares two or more whole numbers and lists every divisor they all share, then highlights the greatest common factor (GCF). It works by finding each number’s complete factor set and keeping only the values present in every set. This is exactly what you need to simplify fractions, split quantities evenly, or reduce ratios to their simplest form.
Formula
common factors = factors(a) ∩ factors(b) ∩ …; GCF = max(common factors)
- a, b, …
- The positive integers being compared (two or more)
- factors(n)
- The complete set of positive divisors of n
- GCF
- Greatest common factor — the largest divisor shared by all inputs
How it works
- Enter at least two positive whole numbers — the calculator needs more than one value to compare.
- It computes the full list of factors for each number and intersects those lists, keeping only the factors that appear in every number.
- The shared factors are shown in ascending order, with the largest of them flagged as the greatest common factor (GCF).
Worked example
Find the common factors of 24, 36, and 60.
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- Keep only the values in all three lists: 1, 2, 3, 4, 6, 12.
Common factors are 1, 2, 3, 4, 6, and 12; the greatest common factor is 12.
Frequently asked questions
- What is the difference between a common factor and the greatest common factor?
- A common factor is any number that divides all the inputs evenly, and there are usually several. The greatest common factor is simply the largest one of those shared divisors.
- Why do I need to enter at least two numbers?
- Common factors describe what a group of numbers share, which only makes sense when comparing more than one value. With a single number, use the factor calculator to list all of its divisors instead.
- Is 1 always a common factor?
- Yes. The number 1 divides every whole number, so it appears in every set of common factors. If 1 is the only shared factor, the numbers are coprime.
- How does this help simplify fractions?
- Dividing both the numerator and denominator by their greatest common factor reduces a fraction to lowest terms in one step. For example, 24/36 both divide by 12 to give 2/3.