Ratio simplifier: the GCD trick behind every clean mix

A ratio is two numbers describing a mix — screen pixels, concrete parts, drink syrup to water. "1024 : 768" and "4 : 3" describe the exact same proportion; the second is just easier to read. Getting from one to the other is one operation: divide both numbers by their greatest common divisor (GCD), the largest number that goes into both exactly.

The method

Find the GCD of the two numbers, then divide both by it. What's left can't be reduced any further, because by definition nothing bigger than the GCD divides both sides.

A real example: 1024 : 768

The GCD of 1024 and 768 is 256. 1024 ÷ 256 = 4 and 768 ÷ 256 = 3, so the ratio simplifies to 4 : 3 — the classic old-monitor aspect ratio, hiding inside a resolution most people never think to reduce.

A real example: doubling a recipe cleanly — 36 : 60

A dressing calls for 36 g of oil to 60 g of vinegar. The GCD of 36 and 60 is 12: 36 ÷ 12 = 3 and 60 ÷ 12 = 5, so the working ratio is 3 : 5. Now scaling to any batch size is a single multiplication — want 400 g of vinegar? That's 80 times the "5" part, so oil is 3 × 80 = 240 g. Reducing first is what makes the scaling arithmetic small.

A real example: paint mix — 250 : 1000

A tin says mix 250 ml of hardener per 1000 ml of base. The GCD of 250 and 1000 is 250: 250 ÷ 250 = 1 and 1000 ÷ 250 = 4, giving 1 : 4. One part hardener to four parts base — the label's numbers were just an unreduced way of saying that.

When it's already simplest: 9 : 16

Not every ratio shrinks. The GCD of 9 and 16 is 1 — they share no factor bigger than 1, which is what "already in lowest terms" means. Modern widescreen video is 16 : 9 for the same reason 4 : 3 survived from 1024 : 768: broadcasters picked numbers with no common factor left to remove, so there is only ever one way to write them.

Finding the GCD without a table of factors

For small numbers, listing factors works. For anything bigger, Euclid's algorithm is faster: divide the larger number by the smaller, keep the remainder, then repeat with the smaller number and that remainder until the remainder hits zero. The last non-zero remainder is the GCD. For 120 and 180: 180 ÷ 120 leaves 60, then 120 ÷ 60 leaves 0 — so the GCD is 60, and 120 : 180 reduces to 2 : 3. (More on the method itself in the GCD & LCM post.)

What a ratio doesn't tell you

A ratio is a proportion, not an amount. "3 : 5" says nothing about whether you're making 8 grams or 8 kilograms of dressing — it only fixes how the parts relate to each other. You still need one real quantity (400 g of vinegar, in the example above) before a ratio turns into a recipe. And a ratio simplifies cleanly only for whole-number inputs; feed it a measurement with rounding already baked in and the "exact" reduced form is only as exact as what you started with.

Run your own numbers

The free Ratio Simplifier finds the GCD and reduces any two whole numbers to lowest terms, entirely on your device.