Ratio of 3 Numbers Calculator

A ratio of three numbers, expressed as A : B : C, shows the relative sizes of three distinct quantities. To simplify this ratio to its lowest terms, the calculator first determines the Greatest Common Factor (GCF) of all three numbers using sequential Euclidean algorithms. Once the GCF is identified, each individual number is divided by this common divisor: A_reduced = A / GCF, B_reduced = B / GCF, and C_reduced = C / GCF. Additionally, the tool allows you to scale these values up or down by a specific multiplier using enlargement or reduction parameters.

Imagine you have a mixture or financial portfolio split into quantities of 4, 6, and 10, and you want to reduce it to its simplest form. First, find the factors of each number: the factors of 4 are (1, 2, 4), the factors of 6 are (1, 2, 3, 6), and the factors of 10 are (1, 2, 5, 10). The greatest common divisor shared by all three numbers is 2. Next, divide each component of the ratio by this GCF: 4 / 2 = 2, 6 / 2 = 3, and 10 / 2 = 5. The fully simplified three-part ratio is therefore 2 : 3 : 5.

Always verify that all quantities share the same unit of measurement before calculating your ratio; mixing units like grams and kilograms will invalidate the output. When dividing a total sum by a ratio (such as splitting $50 into a 2 : 3 : 5 ratio), first sum the ratio parts (2 + 3 + 5 = 10 parts), determine the value of a single part ($50 / 10 = $5 per part), and multiply each ratio number by that unit value ($10, $15, and $25).