Quick start
- Type the fraction, for example 84/126.
- Read the greatest common factor and the simplified fraction.
One-step simplification
Instead of dividing by 2, then 3, then 7 in turn, find the greatest common factor (GCF) once and divide by it. That guarantees the result is fully reduced.
Example: 84/126
Euclid's algorithm: 126 = 1 × 84 + 42, then 84 = 2 × 42 + 0. The last non-zero remainder, 42, is the GCF. Dividing gives 84 ÷ 42 = 2 and 126 ÷ 42 = 3, so 84/126 = 2/3.
How to tell a fraction is fully simplified
A fraction is in lowest terms when the top and bottom share no factor except 1. 9/16 is already simplified even though neither number is prime, because 9 = 3² and 16 = 2⁴ have nothing in common.
Common questions
Does simplifying change the value?
No. 84/126 and 2/3 are the same number written more simply.
What if the top is larger than the bottom?
It still simplifies normally. Use the Mixed Number Calculator if you want it as a mixed number.
Why use Euclid's algorithm?
It finds the GCF quickly even for large numbers, without listing all the factors.