Math · Fractions
Simplify fractions calculator.
Reduce any fraction to lowest terms. The greatest common factor is found step by step with the Euclidean algorithm.
Inputs
Simplified fraction
Enter a numerator and a denominator.
How to simplify a fraction
To simplify a fraction, divide the top and bottom by the highest number that divides into both exactly. That number is the greatest common factor (GCF). A fraction is in lowest terms when the GCF is 1.
Worked example. Simplify 24/108. Repeated division by 2, 2 and 3 gets there: 24/108 = 12/54 = 6/27 = 2/9. The GCF method does it in one step: GCF(24, 108) = 12, and 24 ÷ 12 = 2, 108 ÷ 12 = 9.
More. 10/35 has a GCF of 5 and simplifies to 2/7. 8/12 has a GCF of 4 and simplifies to 2/3.
This tool finds the GCF with the Euclidean algorithm: divide the larger number by the smaller, then repeat with the remainder until the remainder is 0. The last non-zero remainder is the GCF.
Frequently asked questions
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common factor. 24/108 divided top and bottom by 12 is 2/9.
How do I know a fraction is fully simplified?
When the only number that divides both the top and the bottom is 1, the GCF is 1 and the fraction is in lowest terms.
What is the Euclidean algorithm?
A way to find the GCF: divide the larger number by the smaller one, then divide the smaller by the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCF.
Can I simplify by dividing by 2, 3, 5 and so on instead?
Yes. Try dividing top and bottom by small primes until you cannot go further. 24/108 becomes 12/54, 6/27 and then 2/9.
What about negative fractions?
The minus sign moves to the numerator, so 6/-9 is shown as -2/3.
Sources
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For learning
Whole numbers only. For GCF and LCM of several numbers use the GCF and LCM calculator. Results are rounded for display. Check with your teacher's required method when you hand in homework.