How this instrument works
A fraction is in lowest terms when its numerator and denominator share no common factor larger than 1 — dividing both by their greatest common divisor (GCD) gets there in a single step, since whatever factor they shared cancels out of both the top and bottom at once, leaving the smallest whole numbers that still represent the exact same value.
This site already has separate GCD and GCF calculators for finding that single shared-factor number on its own — this page's job is different: it takes that GCD calculation and immediately applies it, handing back the actual REDUCED FRACTION itself (a numerator and a denominator together) rather than just the one number they were divided by.
Reducing to lowest terms never changes what the fraction is actually worth, only how it's written — 24⁄36 and 2⁄3 sit at the identical point on the number line, and confirming that (by cross-multiplying, 24×3=72 and 2×36=72) is a quick sanity check that the reduction was done correctly.
- Enter the fraction's numerator into the Numerator field.
- Enter its denominator into the Denominator field.
- Read Reduced numerator and Reduced denominator — the fraction in its simplest form.
- Multiply the reduced numerator by the original denominator and compare it against the reduced denominator times the original numerator to confirm nothing changed in value.
Worked example — reducing 24⁄36
24 and 36 share a greatest common divisor of 12: dividing both by 12 gives 24÷12=2 and 36÷12=3, so 24⁄36 reduces to 2⁄3 in one step. Checking the value hasn't changed: 24×3=72 and 2×36=72, confirming the two fractions are equal.
A fraction can also already BE in lowest terms: 7 and 13 share no common factor larger than 1 (their GCD is 1), so 7⁄13 comes back unchanged — dividing by 1 never simplifies anything further.
Questions
What does it mean for a fraction to be in lowest terms?
That its numerator and denominator share no common factor greater than 1 — the greatest common divisor of the two numbers is exactly 1, meaning no further whole-number division could simplify it any more than it already is.
How do you reduce a fraction to lowest terms?
Find the greatest common divisor of the numerator and denominator, then divide both by that number — a single division applied to each side is always enough, since the GCD already captures every factor they share.
Does reducing a fraction change its value?
No — dividing both the numerator and denominator by the same nonzero number never changes what the fraction is worth, only how compactly it's written. 24⁄36 and 2⁄3 sit at the exact same point on the number line.
How is this different from the GCD or GCF calculators on this site?
Those pages return just the single greatest-common-divisor number itself; this page takes that same calculation one step further and returns the fully reduced fraction — two numbers, a numerator and a denominator, rather than one.
What if the fraction is already in lowest terms?
Its greatest common divisor is 1, so dividing both numbers by 1 changes nothing — this calculator simply confirms the fraction back to you unchanged, which is itself useful confirmation that no further simplification exists.