Reduce Fraction to Lowest Terms Calculator
Reduce any fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor.
How it works
Reduced fraction = (n ÷ GCD) / (d ÷ GCD), where GCD is the greatest common divisor of n and d
A fraction is in lowest terms when its numerator and denominator share no common factor other than 1. To get there, find the greatest common divisor of the two numbers and divide both by it in a single step. The value of the fraction is unchanged — only the way it is written becomes simpler.
Worked example
For 18/24, the greatest common divisor of 18 and 24 is 6. Dividing both parts by 6 gives 3/4. Because GCD(3, 4) = 1, the fraction 3/4 cannot be reduced any further.
Sources: Euclidean algorithm — Wikipedia
Frequently asked questions
What does "lowest terms" mean?
A fraction is in lowest terms (or simplest form) when the only whole number that divides both the numerator and denominator evenly is 1. At that point it cannot be written with smaller numbers.
How is the greatest common divisor found?
This tool uses the Euclidean algorithm: repeatedly replace 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.
Why divide by the GCD instead of common factors one at a time?
Dividing by the GCD once reaches lowest terms in a single step. Cancelling smaller common factors repeatedly works too, but you have to keep going until nothing else divides evenly.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.