GCF Calculator · Practical guide
Greatest Common Factor of Three Numbers
Enter as many numbers as you like, separated by commas, and get the GCF for the whole set.
At a glance
How It Works for Three or More Numbers
The greatest common factor of a set of numbers is the largest integer that divides every number in the set evenly. For 48, 72, and 120, the GCF is 24: 48 ÷ 24 = 2, 72 ÷ 24 = 3, and 120 ÷ 24 = 5. No larger number divides all three.
Interactive tool
GCF Calculator
Enter your own values, then compare the result with the examples below.
Results
The Pairwise Euclidean Method
You do not need a new technique for three numbers — apply the Euclidean algorithm one pair at a time:
- gcd(72, 48): 72 mod 48 = 24, then 48 mod 24 = 0, so gcd = 24
- gcd(120, 24): 120 mod 24 = 0, so gcd = 24
The calculator performs exactly this chain when you enter a comma-separated list like 48, 72, 120.
Checking with Prime Factorization
- 48 = 2 × 2 × 2 × 2 × 3
- 72 = 2 × 2 × 2 × 3 × 3
- 120 = 2 × 2 × 2 × 3 × 5
The factors common to all three are three 2s and one 3: 2 × 2 × 2 × 3 = 24. Notice the 5 in 120 drops out because the other numbers do not share it.
Practical Uses
Multi-number GCFs show up in real problems: cutting three boards of lengths 48, 72, and 120 inches into equal pieces with no waste means pieces of 24 inches. Simplifying ratios like 48:72:120 also uses the GCF — divide through by 24 to get 2:3:5.
Frequently Asked Questions
Is the GCF of a set always smaller than the numbers?
The GCF is always less than or equal to the smallest number in the set. It equals the smallest number only when that number divides all the others.
How many numbers can I enter at once?
You can enter any list of two or more numbers separated by commas. The calculator chains the Euclidean algorithm across the entire set.
What happens with negative numbers?
The calculator uses absolute values, so the GCF of -12 and 18 is the same as the GCF of 12 and 18, which is 6.
Can the GCF of three numbers be 1?
Yes. If no integer greater than 1 divides all three, the set is coprime as a group. For example, the GCF of 6, 10, and 15 is 1 even though each pair shares a factor.