Lowest Term Calculator
Enter a numerator and denominator to instantly reduce your fraction to its lowest terms. The calculator finds the greatest common divisor (GCD), divides both parts by it, and shows every step of the working. Improper fractions are also displayed as mixed numbers so you can see the result both ways.
Formula
Worked example
To reduce 18/24: find GCD(18, 24). Using the Euclidean algorithm: 24 = 1 x 18 + 6, then 18 = 3 x 6 + 0, so GCD = 6. Divide both parts by 6: numerator 18/6 = 3, denominator 24/6 = 4. Result: 3/4.
What does "lowest term" mean?
A fraction is in its lowest terms (also called simplest form or reduced form) when the numerator and denominator share no common factor other than 1. For example, 3/4 is in lowest terms because 3 and 4 have no common factor, while 6/8 is not because both 6 and 8 are divisible by 2, giving the equivalent but simpler fraction 3/4. Reducing fractions to lowest terms makes them easier to compare, add, subtract, and communicate.
How to reduce a fraction to lowest terms
The standard method uses the Greatest Common Divisor (GCD), sometimes called the Greatest Common Factor (GCF). Find the largest integer that divides evenly into both the numerator and the denominator, then divide both parts by it. For 18/24: the factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The largest shared factor is 6, so 18/24 = (18/6)/(24/6) = 3/4. The Euclidean algorithm, which this calculator uses internally, finds the GCD very efficiently even for large numbers by repeatedly dividing and taking remainders until zero is reached.
Proper fractions, improper fractions, and mixed numbers
A proper fraction has a numerator smaller than its denominator (like 3/4). An improper fraction has a numerator greater than or equal to its denominator (like 7/4 or 8/8). Both types can be simplified to lowest terms using the same GCD method. An improper fraction in lowest terms can also be written as a mixed number by dividing: 7/4 = 1 remainder 3, so it is 1 and 3/4. This calculator shows both forms when the result is improper. To enter a mixed number like 2 3/4, select the "Mixed number" input mode and enter 2 as the whole number, 3 as the numerator, and 4 as the denominator. The calculator converts it to the improper fraction 11/4 before simplifying.
Why reducing fractions matters in everyday maths
Lowest terms fractions appear constantly: cooking recipes scale more intuitively with 1/3 cup than 4/12 cup; carpentry dimensions are cleaner as 3/8 inch than 6/16 inch; probability is clearer as 1/6 than 10/60. In algebra, simplifying rational expressions before multiplying or dividing prevents arithmetic with unnecessarily large numbers. Exam and standardised test answers are typically expected in lowest terms, and the process of simplifying reinforces understanding of divisibility, prime factorisation, and number relationships that form the foundation of many more advanced topics.
Common fractions and their lowest terms
| Original fraction | GCF | Lowest term | Decimal |
|---|---|---|---|
| 2/4 | 2 | 1/2 | 0.5 |
| 4/6 | 2 | 2/3 | 0.667 |
| 6/9 | 3 | 2/3 | 0.667 |
| 4/8 | 4 | 1/2 | 0.5 |
| 6/10 | 2 | 3/5 | 0.6 |
| 8/12 | 4 | 2/3 | 0.667 |
| 9/12 | 3 | 3/4 | 0.75 |
| 10/15 | 5 | 2/3 | 0.667 |
| 12/16 | 4 | 3/4 | 0.75 |
| 15/20 | 5 | 3/4 | 0.75 |
| 18/24 | 6 | 3/4 | 0.75 |
| 20/25 | 5 | 4/5 | 0.8 |
| 24/36 | 12 | 2/3 | 0.667 |
| 25/100 | 25 | 1/4 | 0.25 |
| 50/100 | 50 | 1/2 | 0.5 |
| 75/100 | 25 | 3/4 | 0.75 |
Quick reference for frequently used fractions in everyday arithmetic.
Frequently asked questions
How do I know if a fraction is already in lowest terms?
A fraction is already in lowest terms when the only positive integer that divides both the numerator and the denominator is 1, meaning the GCD of the two numbers is 1. For example, 7/11 is already in lowest terms because 7 and 11 are both prime and share no common factor. If you are unsure, just enter the numbers here and the calculator will confirm it instantly.
What is the difference between GCF and GCD?
GCF (Greatest Common Factor) and GCD (Greatest Common Divisor) are two names for exactly the same thing: the largest positive integer that divides evenly into two or more given numbers. The term GCF is more common in primary and secondary school contexts, while GCD is favoured in higher mathematics and computer science. This calculator uses both labels interchangeably.
Can I simplify a fraction with a negative numerator or denominator?
Yes. The GCD method works the same way for negative fractions. The sign is preserved in the numerator of the result. For example, -6/9 simplifies to -2/3. By convention, the negative sign is kept with the numerator, not the denominator, so you would write -2/3 rather than 2/-3.
What if my fraction is already a whole number (denominator of 1)?
Any fraction with a denominator of 1 is already a whole number and is trivially in lowest terms. For example, 7/1 simplifies to 7. If your original denominator is a factor of the numerator, the result will also reduce to a whole number: 8/4 simplifies to 2/1, which is displayed as just 2.
How do I reduce a mixed number to lowest terms?
Select the "Mixed number" input mode, enter the whole number part separately, then enter the fractional numerator and denominator. The calculator converts the mixed number to an improper fraction (multiply the whole number by the denominator and add the numerator), simplifies that improper fraction to lowest terms, and then converts it back to a mixed number. For example, 2 and 6/9: convert to 24/9, simplify to 8/3, then express as 2 and 2/3.
Why does the calculator divide by the GCF rather than just any common factor?
Dividing by any common factor makes the fraction simpler, but you may need to repeat the process several times before reaching the lowest term. Dividing by the greatest common factor does it in a single step. For example, 24/36 could be divided by 2 to get 12/18, then by 2 again to get 6/9, then by 3 to get 2/3. Dividing by the GCF (12) goes straight to 2/3 in one operation.