How to simplify a ratio by hand and by GCD
What it means to reduce a ratio, how the greatest common divisor does the work, and how to read the decimal and scaled forms this tool shows.
What simplifying a ratio actually means
A ratio compares two quantities, and simplifying it means finding the smallest whole numbers that express the same comparison. The ratio 12:18 and the ratio 2:3 describe the identical relationship; the second is just easier to read and reason about. To reduce a ratio you divide both sides by a number that goes into each of them evenly. Do that with the largest such number and you land on the simplest form in a single step.
The greatest common divisor is the shortcut
The largest number that divides both sides is called the greatest common divisor, or GCD. Rather than test factors one by one, this tool uses Euclid's algorithm, which repeatedly replaces the larger number with the remainder of dividing the two until one becomes zero. For 1920 and 1080 that process lands on 120, and dividing both sides by 120 gives 16:9. The method is fast even for very large numbers and never needs a factor table.
Reading the decimal and knowing its limits
Dividing the first side by the second turns a ratio into a single decimal, which is useful for quick comparison. A 16:9 ratio is about 1.777778, and a taller 4:3 ratio is about 1.333333, so the larger decimal is the wider shape. The tool rounds this decimal to six places for a clean display, meaning a repeating value is an approximation rather than the exact fraction. When the second side is zero there is no decimal at all, because dividing by zero is undefined.
Scaling a ratio up or down
Once a ratio is in lowest terms you often need it at a specific size, and that is what scaling does. Multiplying both sides by the same factor keeps the proportion but changes the absolute numbers, so 16:9 scaled by 120 returns to 1920:1080. Scaling is how you resize an image while keeping its shape, double a recipe, or convert a map ratio to real distances. Because the tool multiplies the exact values you give, a fractional factor can leave a fractional side, which is mathematically correct even if it looks unusual.