Lowest Term Calculator — Simplify a Fraction
Enter any fraction — positive, negative, or improper — and get it reduced to lowest terms in one click. The calculator shows every step of the Euclidean GCD algorithm so you can follow exactly how the simplification works.
Divided numerator and denominator by GCD = 6
12 = 0 × 18 + 12
18 = 1 × 12 + 6
12 = 2 × 6 + 0
Greatest Common Divisor
Divide numerator and denominator by 6
- 1
Find GCD of |numerator| and |denominator|
GCD(12, 18) = 6 - 2
Divide denominator by GCD
18 ÷ 6 = 3 - 3
Divide numerator by GCD
12 ÷ 6 = 2
How does this calculator work?
Divide both numerator and denominator by GCD(numerator, denominator) to get the fraction in lowest terms. GCD is found in seconds using the Euclidean algorithm. If GCD = 1 the fraction is already irreducible. Works for positive, negative and improper fractions — decimal inputs are rounded to integers.
Formula
How this is calculated
A fraction n/d is in lowest terms (simplest form) when the numerator and denominator share no common factor other than 1, i.e. their GCD is 1. To reduce a fraction, divide both the numerator and denominator by their GCD: the result is an equivalent fraction with the smallest possible integers.
The GCD is found with the Euclidean algorithm: divide the larger number by the smaller, take the remainder, then repeat with (smaller, remainder) until the remainder is zero — the last non-zero remainder is the GCD. For example, GCD(12, 18): 18 = 1 × 12 + 6, then 12 = 2 × 6 + 0, so GCD = 6. Dividing 12/18 by 6/6 gives 2/3.
The calculator handles negative fractions by keeping the sign on the numerator (denominator is always made positive). Improper fractions (numerator ≥ denominator) are reduced but not converted to mixed numbers — use a mixed-number converter if you need that form. Inputs are rounded to the nearest integer since fractions are defined only for integers.
Frequently asked questions
A fraction is in lowest terms (also called simplest form or irreducible form) when no integer other than 1 divides both the numerator and denominator evenly. For example, 6/10 simplifies to 3/5 because GCD(6, 10) = 2. Once the GCD is 1, the fraction cannot be reduced further.
List the prime factors of both numerator and denominator, then cancel any shared factors. For example, 18/24: 18 = 2×3² and 24 = 2³×3, so the shared factors are 2×3 = 6, giving 18/24 = 3/4. The Euclidean algorithm (shown step-by-step here) is usually faster than factoring for large numbers.
By convention, the denominator of a fraction in standard form is always positive. If you enter a negative denominator (e.g. 3/−6), the calculator moves the negative sign to the numerator and returns −1/2, which is the standard representation.
Also known as
TG we-Calculate Editorial Team. (2026). Lowest Term Calculator — Simplify a Fraction [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lowest-term-calculator
TG we-Calculate Editorial Team. "Lowest Term Calculator — Simplify a Fraction." TG we-Calculate. 2026. https://we-calculate.com/calculator/lowest-term-calculator.
TG we-Calculate Editorial Team, "Lowest Term Calculator — Simplify a Fraction," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lowest-term-calculator
@misc{wecalculate_lowest_term_calculator, title = {Lowest Term Calculator — Simplify a Fraction}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lowest-term-calculator}}, year = {2026}, note = {TG we-Calculate} }
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