How do I use GCF to simplify fractions?

Divide both numerator and denominator by their GCF. For example, to simplify 48/72, find GCF(48,72) = 24, then 48÷24 = 2 and 72÷24 = 3, so 48/72 = 2/3.

What's the relationship between GCF and LCM?

For two numbers a and b: GCF(a,b) × LCM(a,b) = a × b. This relationship helps you find one if you know the other.

What if the GCF is 1?

When GCF = 1, the numbers are called relatively prime or coprime. This means they share no common factors other than 1. For example, GCF(15,28) = 1.

Can GCF be larger than the smallest number?

No, the GCF cannot be larger than the smallest number in the set. In fact, the GCF of any set of numbers is always less than or equal to the smallest number in that set.

GCF Calculator – Greatest Common Factor

Find the greatest common factor (GCF) or greatest common divisor (GCD) of two or more numbers. Essential for simplifying fractions and solving math problems.

GCF Calculator – Greatest Common Factor

Find the greatest common factor (GCF) or greatest common divisor (GCD) of two or more numbers. Essential for simplifying fractions and solving math problems.

Numbers*

Enter numbers separated by commas

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Understanding Greatest Common Factor

The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), is the largest positive integer that divides all given numbers without remainder. It's fundamental for simplifying fractions and solving various mathematical problems.

Applications of GCF

Common uses for GCF:

Simplifying fractions to lowest terms
Reducing ratios to simplest form
Dividing objects into equal groups
Finding common tile sizes for flooring
Solving Diophantine equations
Cryptography and number theory

How to Use This Calculator

Follow these simple steps to get accurate results:

Enter your numbers
Click the "Calculate" button to see your results
Review the detailed breakdown and explanation

Why Use Our GCF Calculator – Greatest Common Factor?

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Instant, accurate calculations with professional formulas
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Educational content to help you understand the results

Frequently Asked Questions

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