Guide · Lowest terms
Simplify Fractions Calculator
Updated: June 2026
Two fractions can describe the same amount while looking completely different. 18/24 and 3/4 are equal, but only one of them is in lowest terms. Simplifying — also called reducing — means rewriting a fraction with the smallest whole numbers possible, which makes it easier to read, compare and compute with.
Free · No upload · Instant in the browser
What “lowest terms” means
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. As long as some number divides both, you can keep shrinking the fraction without changing its value.
3 and 4 share no factor → done
The value never moves; you are just choosing the simplest pair of numbers that still hits the same point on the number line.
The greatest common divisor method
The fastest route is to divide both numbers by their greatest common divisor (GCD) in a single step.
gcd(45, 60) = 15
45 ÷ 15 = 3, 60 ÷ 15 = 4 → 3/4
If finding the GCD by inspection is hard, the Euclidean algorithm gets it quickly: divide the larger by the smaller, keep the remainder, repeat until the remainder is zero. The last non-zero divisor is the GCD.
The peel-off-factors method
If you prefer small steps, repeatedly cancel any factor you can see. It takes longer but never requires you to find the full GCD up front.
Both methods reach the same destination. The single-GCD route is tidier; the peel-off route is more forgiving when the numbers are unfamiliar.
Prime factorisation
For tricky cases, break both numbers into primes and cancel the shared ones. This also reveals exactly why a fraction does or does not simplify.
24 = 2 × 2 × 2 × 3
shared: 2 × 3 = 6
18/24 = 3/4
If the two factor lists have nothing in common, the fraction is already in lowest terms — there is nothing to cancel.
Why bother simplifying?
- Comparison — 3/4 versus 5/6 is far easier to judge than 18/24 versus 20/24.
- Smaller arithmetic — reduced fractions keep later multiplication manageable.
- Standard answers — exams and recipes expect lowest terms.
- Cleaner decimals — the decimal of 3/4 is obvious; 18/24 hides it.
A reduced fraction is the canonical form: every equal fraction collapses to the same lowest-terms pair, so it is the natural way to check whether two fractions are really the same.
Frequently asked questions
How do I simplify 18/24?
Divide both by their greatest common divisor, 6, to get 3/4.
What is the greatest common divisor?
It is the largest whole number that divides both the numerator and denominator exactly. Dividing by it reduces the fraction in one step.
How do I know a fraction is fully simplified?
When the numerator and denominator share no common factor other than 1, the fraction is in lowest terms.