Fraction Simplifier
Reduce any fraction to lowest terms with the greatest common divisor, plus the mixed number, the decimal value and every step of Euclid's algorithm.
Simplifying a fraction means dividing the top and bottom by the largest number that goes into both — their greatest common divisor (GCD). The result is an equivalent fraction in lowest terms, such as 18/24 = 3/4. This simplifier finds the GCD with Euclid's algorithm, shows every division step, and also gives the mixed number and the decimal value.
How to use this tool
- Enter the numerator (top number).
- Enter the denominator (bottom number); it cannot be 0.
- Read the simplified fraction and the GCD that was divided out.
- Follow the Euclid table to see how the GCD was found.
Formula
a/b = (a ÷ g) / (b ÷ g), where g = gcd(a, b)
Euclid's algorithm finds g by repeatedly replacing the pair (a, b) with (b, remainder of a ÷ b) until the remainder is 0; the last non-zero remainder is the GCD. A fraction is already in lowest terms when g = 1. A minus sign is moved to the numerator, and a whole-number result such as 100/25 = 4 is shown without a denominator.
Example
Simplify 1071/462. Euclid: 1071 = 2 × 462 + 147, then 462 = 3 × 147 + 21, then 147 = 7 × 21 + 0, so the GCD is 21. Dividing both numbers by 21 gives 51/22, which is the mixed number 2 7/22, or about 2.318182 as a decimal.
Frequently asked questions
How do I know a fraction is fully simplified?
When the numerator and denominator share no factor other than 1. 51/22 is final because 51 = 3 × 17 and 22 = 2 × 11 have no prime in common.
Can I simplify in several smaller steps?
Yes — 18/24 → 9/12 → 3/4 works as well. Dividing by the GCD does it in one step and guarantees you have finished.
What happens with negative fractions?
−8/12 and 8/−12 both simplify to −2/3. The calculator always puts the sign on the numerator.
Can I enter decimals?
Yes. 0.75/1.5 is first scaled to 75/150, then reduced to 1/2.
Last updated: 2026-10-30