Math Tool

Common Factor Calculator

Find all common factors, the greatest common factor (GCF), and least common multiple (LCM) of two or more integers.

Enter integers (comma-separated)

Greatest Common Factor (GCF)

Count of numbers3

All common factors1, 2, 3, 4, 6, 12

Least common multiple (LCM)360

What is the Common Factor Calculator?

A common factor is a whole number that divides evenly into two or more integers. The greatest common factor (GCF) is the largest such number. The least common multiple (LCM) is the smallest positive integer divisible by all input numbers. Together, GCF and LCM reveal the hidden structure of how numbers relate.

How it works

Enter two or more integers separated by commas. The calculator uses the Euclidean algorithm to find the GCF by repeatedly replacing the larger number with the remainder of division until reaching zero. It then lists all common factors by finding divisors of the GCF, and computes the LCM using the formula lcm(a, b) = (a × b) / gcd(a, b), extended to multiple numbers.

GCF = gcd(n₁, n₂, ..., nₖ) using Euclidean algorithm; LCM = (n₁ × n₂) / gcd(n₁, n₂) extended recursively

The Euclidean algorithm works by dividing the larger number by the smaller and repeating with the divisor and remainder until the remainder is zero; the last non-zero remainder is the GCF. The LCM formula exploits the relationship that the product of two numbers equals their GCF times their LCM.

Examples

Input	Result	Notes
12, 18	GCF = 6; LCM = 36	12 = 2² × 3 and 18 = 2 × 3², so their GCF is 2 × 3 = 6 and LCM is 2² × 3² = 36.
24, 36, 60	GCF = 12; LCM = 360	All three share factors 1, 2, 3, 4, 6, 12; their LCM is 360 = 2³ × 3² × 5.
100, 150, 200	GCF = 50; LCM = 600	Common factors are 1, 2, 5, 10, 25, 50; LCM is 2³ × 3 × 5² = 600.

How to use the Common Factor Calculator

Enter two or more positive integers, separated by commas.

The calculator applies the Euclidean algorithm to find the GCF iteratively.

It extracts all divisors of the GCF to show every common factor.

Using the GCF values, it computes the LCM recursively across all numbers.

The result displays the GCF as the primary answer and the LCM and all factors in the statistics panel.

Review the common factors to understand which divisors work for all your numbers.

Benefits

Simplify fractions by dividing numerator and denominator by their GCF.

Add or subtract fractions with different denominators using the LCM as the common denominator.

Solve real-world problems involving divisibility, scheduling, and distribution.

Understand prime factorization and how numbers relate through their common factors.

Avoid manual trial-and-error and reduce errors in mathematical computations.

Verify your work in homework, tests, and number theory applications.

Tips & common mistakes

Common mistakes

Forgetting to include 1 as a common factor—every positive integer is divisible by 1.

Confusing GCF with LCM; GCF is the largest shared divisor, while LCM is the smallest shared multiple.

Entering zero or negative numbers; the calculator works with positive integers only.

Assuming the GCF of two coprime numbers (like 7 and 11) is 1—which is correct, but their LCM is their product.

Tips

For two numbers, GCF and LCM are related by the formula: GCF × LCM = n₁ × n₂.

If one number is a multiple of another, the GCF is the smaller number and the LCM is the larger.

Prime numbers have a GCF of 1 with any other number not a multiple of that prime.

Use the GCF to reduce fractions and the LCM to find a common denominator for fraction arithmetic.

Frequently asked questions

What is the difference between GCF and LCM?

GCF (greatest common factor) is the largest number that divides all inputs. LCM (least common multiple) is the smallest number divisible by all inputs. If GCF = 12 and LCM = 360, then 12 divides all numbers and all numbers divide 360.

Why is the GCF of 7 and 11 equal to 1?

7 and 11 are both prime numbers. Two different primes share only 1 as a common factor, so they are coprime. Their LCM is 7 × 11 = 77.

Can I use this calculator for negative integers?

The calculator works with the absolute values of integers, so −24 and 24 are treated identically. GCF and LCM are always positive.

How do I simplify a fraction using the GCF?

Find the GCF of the numerator and denominator, then divide both by that GCF. For example, 24/36 has GCF = 12, so it simplifies to 2/3.

What is the relationship between GCF, LCM, and prime factorization?

The GCF includes each prime factor raised to the minimum power across all numbers; the LCM includes each prime raised to the maximum power. This explains why GCF × LCM = n₁ × n₂.

How do I find a common denominator for adding fractions?

Compute the LCM of the denominators. For example, to add 1/12 + 1/18, find LCM(12, 18) = 36, then rewrite as 3/36 + 2/36 = 5/36.