Reduce any fraction to lowest terms and see exactly which greatest common factor got it there.

How to Use the Simplifying Fractions Calculator

Enter a numerator and a denominator; the reduced fraction comes back along with the greatest common factor used to get there, or a note that the fraction was already in simplest form.

Finding the greatest common factor by listing every factor of both numbers works, but it's slow once the numbers get large. This calculator uses the Euclidean algorithm instead — over 2,000 years old, from Euclid's Elements, and still the fastest common way to do it by hand or by machine:

gcd(a, b) = gcd(b, a mod b), repeat until b = 0

Divide the larger number by the smaller and keep only the remainder. Replace the larger number with that remainder, repeat, and stop once the remainder hits zero — the last non-zero remainder is the GCD. For 24 and 36: 36 mod 24 is 12, then 24 mod 12 is 0, so the GCD is 12, and 24/36 reduces to 2/3.

Dividing both the numerator and denominator by that same number is what actually simplifies the fraction — it changes how the value is written, not the value itself, since dividing both halves of a ratio by the same number leaves the ratio unchanged. A GCD of 1 means there's nothing left to divide out — the fraction was already as simple as it gets.

This is the same mechanism the Fraction Calculator and its dedicated Add/Subtract/Multiply/Divide siblings lean on to keep their own results in lowest terms — it's just not usually shown as its own step there. Negative numbers work the same way; the sign carries through to the numerator, and the denominator stays positive by convention.