The greatest common factor (GCF/GCD) is the largest positive integer that divides every number in your list. Enter two or more integers and read the GCF plus a prime-factor row per number—shared primes are highlighted so you can match textbook factor trees or short division.
What it means
Any d that divides all inputs is a common factor; the largest is the GCF. For 48 and 18, common factors are 1, 2, 3, 6 → GCF = 6. Reducing ( rac{18}{48}) means dividing top and bottom by 6.
How to use
- Tap an example set or type integers (commas, spaces, or line breaks).
- Preview pills show parsed values; append one integer or clear the list anytime.
- Read the hero GCF and highlighted shared primes on the right.
- For LCM on the same list, use the LCM calculator; full factorization of one n → prime factorization.
By hand (prime method)
48 = 2⁴×3, 18 = 2×3² → take each shared prime to the lower power → 2×3 = 6.
Examples
12 & 18 → GCF 6; 24, 36, 60 → GCF 12; coprime 8 & 15 → GCF 1.
Notes
At least two integers, no zeros; negatives use |n|. Keep homework-sized inputs for huge LCM companions.
Frequently asked questions
Is GCF the same as GCD?
Yes—GCF and GCD are the same: the largest positive integer dividing every number in your list. Smaller common factors exist too, but only one greatest.
How does GCF relate to simplifying fractions?
Simplest form means dividing numerator and denominator by GCF(a,b). For ( rac{18}{48}), GCF 6 gives ( rac{3}{8}).
Why highlight prime factors?
In the prime method, take each shared prime to the lower power and multiply—that is the GCF. Highlights match that step vs factor trees.
How do I enter the integers?
Use example sets, a comma/space list, preview pills, append one integer, or clear—same layout as the average calculator’s data area.
How many numbers? Can I use zero?
At least two integers. Zero is not allowed in the list. Negatives factor on |n|; the GCF shown is non-negative.
What if two numbers are coprime?
Coprime means GCF = 1. Highlights may show no shared primes; the hero result is 1.
How does this fit with LCM and prime factorization?
For positives a,b: a×b = GCF×LCM. Factor one n on prime factorization; LCM on LCM calculator.
Can I save my inputs?
Yes. Copy link below the form keeps your current inputs so you can share the scenario or save it for later.