Simplifying Fractions Calculator
Reduce a single fraction to its lowest terms using the greatest common factor, and see the GCF used, the mixed number, and the decimal.
In lowest terms
2/3
Greatest common factor used: 4.
As a mixed number
2/3
As a decimal
0.666666666667
Step by step
- Greatest common factor of 8 and 12 is 4
- Divide top and bottom by 4
- Result: 2/3
How it works
Simplifying a fraction means dividing the top and bottom by the same number until they share no common factor except 1. The largest number you can divide both by is the greatest common factor, or GCF. For 8/12 the GCF is 4, and dividing both by 4 gives 2/3.
This tool finds the GCF with the Euclidean algorithm — a fast, exact method that repeatedly takes remainders — so it works cleanly even for big numerators and denominators. It shows you which GCF it used, so the reduction isn't a black box.
If the fraction is already in lowest terms, the GCF comes back as 1 and nothing changes, and the tool says so. You also get the mixed-number and decimal forms. Negative fractions keep their sign, which sits on the numerator after reducing.
Frequently asked questions
What is the greatest common factor?
It's the largest whole number that divides both the numerator and denominator with no remainder. Dividing both by the GCF in one step takes a fraction straight to its lowest terms.
How do I know a fraction is fully reduced?
When the GCF of the top and bottom is 1, there's nothing left to cancel and the fraction is in lowest terms. The tool tells you when that's the case so you're not left guessing.
Does it work with negative fractions?
Yes. A fraction like -8/12 reduces to -2/3. The sign is preserved and shown on the numerator of the simplified result.