Where GCF is used
Simplifying fractions, reducing ratios, tiling problems (largest square tile that fits evenly) and scheduling events that share cycles all rely on the GCF.
GCF Calculator
Greatest common factor (HCF/GCD) of two integers via the Euclidean algorithm.
Enter your details and press Calculate to see results.
Formula
GCD(a, b) = GCD(b, a mod b), repeating until b = 0
Example
GCD(48, 36): 48 mod 36 = 12 → GCD(36, 12): 36 mod 12 = 0 → GCF = 12.
Advertisement
Frequently asked questions
Is GCF the same as HCF?
Yes — greatest common factor and highest common factor are different names for the same concept (also called GCD).
What if one number divides the other?
The larger number's divisor relationship wins: GCF(12, 36) = 12.
Related calculators
Scientific Calculator
Full expression calculator with parentheses, powers, roots, trigonometry, logarithms and constants π and e.
Percentage Calculator
Calculate X% of Y, find what percent one number is of another, and solve percentage increase problems in one place.
Percentage Increase Calculator
Find the percentage increase between an original value and a new value, including the absolute change.
Exponent Calculator
Raise any base to any power, including negative and fractional exponents.
Percentage Decrease Calculator
Work out how much a value dropped in percent terms, with the absolute reduction shown alongside.
Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers, with results automatically simplified.