How do you simplify a fraction?

To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. The GCD is the largest whole number that divides evenly into both values. For example, to simplify 24/36, the GCD of 24 and 36 is 12, so divide both by 12 to get 2/3. A fraction is in its lowest terms when the GCD of the numerator and denominator is 1.

What is the greatest common divisor (GCD)?

The greatest common divisor (also called the highest common factor or HCF) is the largest positive integer that divides both numbers without leaving a remainder. It is commonly calculated using the Euclidean algorithm, which repeatedly replaces the larger number with the remainder of dividing it by the smaller number until the remainder is zero. The last non-zero value is the GCD.

When is a fraction already in its simplest form?

A fraction is already in its simplest (or lowest) form when the only number that divides both the numerator and denominator without remainder is 1, meaning their GCD is 1. For example, 3/7 is already in its lowest form because 3 and 7 share no common factors other than 1.

Simplify Fractions Calculator

This calculator reduces any fraction to its lowest terms by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it. A fraction is in its simplest or lowest form when the numerator and denominator share no common factors other than one, meaning no further reduction is possible. Simplifying fractions makes them easier to compare, add, subtract and understand, and it is a foundational skill in school mathematics and any field that involves ratios, proportions or probability. The GCD is found using the Euclidean algorithm, one of the oldest algorithms in mathematics, which works by repeatedly replacing the pair (a, b) with (b, a mod b) until the remainder is zero, at which point the last non-zero value is the GCD. Dividing both the numerator and denominator by the GCD produces an equivalent fraction in lowest terms because you are multiplying both parts of the fraction by the same value (the reciprocal of the GCD), which leaves the ratio unchanged. To use the calculator, enter the numerator and denominator of your fraction. You can include a negative numerator to represent a negative fraction. The calculator returns the simplified fraction, the GCD it used, and the decimal equivalent. If the fraction is already in its simplest form, the GCD will be 1 and the fraction will display unchanged. This tool suits students, teachers, and anyone working with ratios or probability values. The denominator cannot be zero.

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Numerator

Denominator

2/3

simplified fraction

GCD used12

Decimal0.6667

Original24/36

How it works

The Euclidean algorithm finds the GCD by repeatedly applying: GCD(a, b) = GCD(b, a mod b) until the remainder is zero. The last non-zero remainder is the GCD. Both the numerator and denominator are then divided by the GCD. If the denominator of the result is negative, the signs are flipped so the negative sign is always expressed in the numerator. A GCD of 1 means the fraction was already in its lowest terms.

Worked example

To simplify 24/36: apply the Euclidean algorithm: GCD(36, 24) = GCD(24, 12) = GCD(12, 0) = 12. Divide both by 12: numerator 24 ÷ 12 = 2, denominator 36 ÷ 12 = 3. The simplified fraction is 2/3. As a decimal: 2 ÷ 3 = 0.6667. The fraction cannot be reduced further because GCD(2, 3) = 1.

Related calculators

Mixed Numbers Calculator: add, subtract, multiply or divide mixed numbers.
Percent to Fraction: convert a percentage to its simplest fraction form.
Long Division Calculator: find the quotient and remainder with step-by-step working.
Percentage Calculator: work out percentages, changes and parts of a whole.

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