Inputs
Adjust the assumptions to match your scenario. Results update instantly.
Results
Primary outputs and comparison insights are built from the current inputs.
GCF
12
Greatest common factor.
LCM
72
Least common multiple.
Product
864
Product of the two numbers.
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How this GCF Calculator works
The GCF Calculator finds the greatest common factor and least common multiple of two integers using the Euclidean algorithm. Enter number 1 and number 2 to estimate gcf, lcm, and product. The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision.
Quick guide
Jump to the section you need, then return to the gcf calculator.
Inputs
- First positive integer.
- Second positive integer.
Outputs
- Greatest common factor.
- Least common multiple.
- Product of the two numbers.
Assumptions
- Inputs are positive integers.
- Uses the Euclidean algorithm for efficiency.
Tips
- GCF is used for simplifying fractions.
- LCM is used for finding common denominators.
GCF Calculator formula guide
Use these gcf calculator formulas to audit the output or explain it to someone else.
2 formulas
GCF Calculator examples
Review a ready-made gcf calculator scenario, copy it, then tweak inputs to match your case.
Example
Fraction simplification
Inputs
- Example input Number 1: 48
- Example input Number 2: 18
Outputs
- Example result GCF: 6
- Example result LCM: 144
- Example result Product: 864
GCF of 48 and 18 is 6, so the fraction 48/18 simplifies to 8/3.
GCF by second number
| Number 2 | GCF | LCM |
|---|---|---|
| 26 | 2 | 312 |
| 31 | 1 | 744 |
| 36 | 12 | 72 |
| 41 | 1 | 984 |
| 46 | 2 | 552 |
GCF × LCM = Product of the two numbers.
GCF pattern
Focus point
26
2
Position
#1 of 5
Original order
Share of total
11.11%
Total: 18
GCF × LCM = Product of the two numbers.
References
- Euclidean algorithm for GCD
- Number theory fundamentals
Learn more
Guides connected to the gcf calculator
Use these short guides when you want the decision framework behind the numbers, not just the raw output.
Category guide
Math Calculator Guide
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FAQ
GCF Calculator FAQ
What does the GCF Calculator do?
The GCF Calculator finds the greatest common factor and least common multiple of two integers using the Euclidean algorithm. Enter number 1 and number 2 to estimate gcf, lcm, and product. The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision. It is part of our math toolkit.
What inputs do I need?
Typical inputs include First positive integer., Second positive integer..
How are the results calculated?
We follow the formulas and assumptions outlined in the "How this calculator works" section. You will see outputs like Greatest common factor., Least common multiple., Product of the two numbers..
Can I share or download the results?
Use the Copy link or Print buttons to share your results. If a table or chart appears, you can download the data as CSV.
Is my data stored?
No. Calculations run in your browser and we do not store your inputs.
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