Factor Ratio Calculator
Enter two numbers or a ratio to simplify it, find the GCF, and see equivalent ratios with a visual bar comparison.
Simplified Ratio
Ratio Bar Comparison
Equivalent Ratios
Step-by-Step
What Is a Factor Ratio?
A factor ratio expresses the relationship between two quantities in simplified form. To simplify a ratio you divide both terms by their Greatest Common Factor (GCF). This process is sometimes called "factoring out" the common factor — hence the name factor ratio.
Simplified ratios are essential in recipes (scaling ingredients), map reading (distance conversions), mixing solutions (chemistry), financial comparisons (debt-to-income), and statistical analysis (odds and probabilities).
Key Concepts
Greatest Common Factor
Largest number dividing both terms
Simplified Form
Both terms divided by GCF
Equivalent Ratios
Multiply both terms by same n
How to Use the Factor Ratio Calculator
Simplify any ratio in three easy steps.
Enter Terms
Type the two numbers that make up your ratio — for example 24 and 36.
Simplify
Click "Simplify Ratio" to find the GCF and reduce both terms to their simplest form.
Explore
View the visual bar comparison, browse equivalent ratios, and read through the step-by-step breakdown.
Worked Examples
Four ratio simplification problems with full solutions.
1Simplify 12 : 8+−
2Simplify 45 : 60+−
3Simplify 100 : 250+−
4Simplify 7 : 7+−
Frequently Asked Questions
Common questions about ratios and simplification.
What is a ratio?+−
A ratio is a comparison of two quantities expressed as a:b or a/b. It shows how many times one value contains or is contained within another. For example, 3:4 means for every 3 of one quantity, there are 4 of another.
How do you simplify a ratio?+−
To simplify a ratio, find the Greatest Common Factor (GCF) of both numbers, then divide each term by the GCF. For example, 12:8 → GCF is 4 → 12÷4 : 8÷4 = 3:2.
What are equivalent ratios?+−
Equivalent ratios are ratios that represent the same relationship. You get them by multiplying (or dividing) both terms by the same non-zero number. For example, 2:3 = 4:6 = 6:9 = 8:12.
What is the difference between a ratio and a fraction?+−
A ratio compares two quantities (part-to-part or part-to-whole), while a fraction specifically represents a part of a whole. The ratio 3:5 can represent 3 boys to 5 girls, whereas 3/8 represents 3 out of 8 total students.
Can a ratio have more than two terms?+−
Yes! Ratios can compare three or more quantities, e.g. 2:3:5. This calculator focuses on two-term ratios, but the same simplification principle applies — divide every term by their common GCF.
How are ratios used in real life?+−
Ratios appear in cooking (ingredient proportions), maps (scale ratios), finance (debt-to-income), science (concentration), and art (golden ratio ≈ 1:1.618). Simplifying ratios makes comparisons clearer.
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