Calculate greatest common factor for multiple values using advanced, intuitive interface online. View stepwise Euclidean and prime factorization methods for full clarity and confidence. Export results, analyze examples, and support learning in classroom environments everywhere. Master factors quickly, accurately, confidently with transparent calculations shown.
Enter at least two non-zero integers separated by commas or spaces. Choose preferred methods and extra insights to explore more number relationships.
| Set | Input Numbers | GCF | LCM | Notes |
|---|---|---|---|---|
| Example 1 | 12, 18 | 6 | 36 | Common factors 1, 2, 3, 6; largest is 6. |
| Example 2 | 24, 60, 96 | 12 | 1920 | Using Euclidean or prime factors gives identical greatest common factor. |
| Example 3 | 35, 63, 91 | 7 | 31885 | All share prime factor 7; remaining factors differ. |
This tool highlights how greatest common factor and least common multiple complement each other. Use combined outputs to structure schedules, group items, or synchronize repeating events accurately.
By decomposing every number into its prime building blocks, the calculator reveals shared structure. This supports deeper learning of divisibility rules, exponent patterns, and factor trees.
Ideal for demonstrations, quick quizzes, and guided practice sessions. Teachers can project step boxes and example tables to verify solutions live while explaining reasoning.
Unlike basic tools, this calculator handles longer lists confidently. It is suitable for fraction sets, ratios, batching problems, and other multi-number scenarios together.
For two integers a and b, repeatedly apply: a = b × q + r, then replace a with b and b with r, until r = 0. The last non-zero remainder is gcd(a, b).
For multiple numbers, the process is extended as gcd(a, b, c) = gcd(gcd(a, b), c).
Factor each number into primes. The greatest common factor is the product of primes common to all numbers, each raised to the smallest exponent appearing across the factorizations.
For two numbers, lcm(a, b) = |a × b| / gcd(a, b). For several numbers, apply iteratively. This relationship is used to provide consistent combined insights.
Tip: Enable all options to turn this into a compact number theory toolkit.
You can use any positive or negative integers, excluding zero. The tool automatically converts values to positive form because greatest common factor is always non-negative.
Greatest common factor describes the largest shared divisor among numbers. With only one number, every divisor of that number qualifies, so comparison between multiple integers is essential.
The GCF is the largest number dividing all inputs exactly. The LCM is the smallest number that all inputs divide into. Our tool can show both using consistent, linked formulas.
Prime factorization steps help when teaching concepts or handling smaller numbers. They visually show shared primes and powers, making it easier to justify each stage of the greatest common factor calculation.
Listing divisors is useful for manual verification and beginner learning. For larger numbers, results are capped for performance while still illustrating the structure needed to understand common factors clearly.
The first value is treated as numerator and the second as denominator. The calculator divides both by their greatest common factor, returning an equivalent fraction in simplest terms automatically.
Yes. It shows every step using standard, widely accepted methods. Use it to confirm answers, explore alternative methods, and strengthen understanding before solving problems independently.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.