GCF Calculator
Use this GCF calculator to find the greatest common factor of two or more positive whole numbers.
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How to Use the GCF Calculator
Enter two or more integers to find their greatest common factor.
Practical Example
For 24 and 36, the GCF is 12 because 12 is the largest integer that divides both values exactly.
Factors That Affect the Result
Use whole numbers and consistent signs. Zero and negative inputs require careful interpretation, although the common-factor magnitude remains based on integer divisibility.
Frequently Asked Questions
Is GCF the same as GCD?
Yes. Greatest common factor and greatest common divisor describe the same concept.
Can the GCF be 1?
Yes. Such numbers are relatively prime.
Can I enter more than two numbers?
Yes, when supported by the input field.
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What the Greatest Common Factor Means
The greatest common factor (GCF) is the largest positive integer that divides each selected integer without leaving a remainder. For example, the factors shared by 18 and 24 include 1, 2, 3, and 6, so their GCF is 6.
Ways to Find the GCF
For small numbers, listing factors is straightforward. Prime factorization finds the prime factors shared by all values and multiplies the common factors with the lowest exponents. The Euclidean algorithm is efficient for larger integers because it repeatedly uses division and remainders until the remainder becomes zero.
Where GCF Is Useful
GCF is commonly used to simplify fractions, factor algebraic expressions, divide quantities into the largest equal groups, and solve ratio problems. If the GCF of two integers is 1, the numbers are relatively prime. When negative inputs are considered, the factor is normally reported as a positive value. Zero requires special handling: the GCF of zero and a nonzero integer is the absolute value of the nonzero integer, while the GCF of zero and zero is generally undefined.