Find the Greatest Common Factor (GCF) of two or more whole numbers, the largest number that divides all of them with no remainder.
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The Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), is the largest whole number that divides every number in your list with no remainder. This calculator uses the Euclidean algorithm, repeatedly applying the fact that the GCF of two numbers also divides their difference, an efficient method that avoids having to list out every factor by hand.
GCF and LCM (Least Common Multiple) answer opposite kinds of questions: GCF finds the largest number that divides into your numbers, while LCM finds the smallest number that all your numbers divide into. Our LCM Calculator computes both figures together if you need them side by side.
For 24, 36 and 60: the Euclidean algorithm first finds GCF(24, 36) = 12, then finds GCF(12, 60) = 12 (since 12 divides evenly into 60). So the GCF of all three numbers is 12, the largest number that divides evenly into 24, 36 and 60 with no remainder.
Confusing GCF with LCM, GCF is always less than or equal to the smallest number entered, while LCM is always greater than or equal to the largest, checking a result against that rule catches most mix-ups.
Listing out every factor by hand for large numbers, this gets slow and error-prone quickly, the Euclidean algorithm this calculator uses finds the GCF in a handful of steps regardless of how large the numbers are.
Entering non-whole or negative numbers, GCF is only defined for positive whole numbers, this calculator requires all entries to be positive integers.
Yes, Greatest Common Factor (GCF) and Greatest Common Divisor (GCD) refer to exactly the same thing, GCF is the more common term in school-level math, while GCD is more common in number theory and computer science.
That's a valid result, it means the numbers are 'coprime', and this calculator will correctly show a GCF of 1.
Yes, enter as many numbers as you'd like, separated by commas or spaces, and this calculator will find the GCF across all of them at once.
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