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Calculate the greatest common divisor of two whole numbers instantly and review the reduced pair plus coprime status.
Calculate the greatest common divisor
Enter two whole numbers to find their greatest common divisor instantly in your browser.
Find the largest shared factor between two whole numbers
Use this GCD calculator when you need the greatest common divisor (GCD), also called the greatest common factor (GCF) or highest common factor (HCF), for two integers. It works well for quick arithmetic checks, factor comparisons, and preparing values for fraction or ratio reduction.
Enter two whole numbers to calculate the greatest common divisor instantly.
Greatest common divisor result
Review the GCD first, then compare the normalized values, reduced pair, and coprime state.
No result
Enter whole numbers to calculate the GCD.
Review the GCD, reduced pair, and coprime state here.
How to use the GCD calculator
- Enter the first whole number you want to compare.
- Enter the second whole number.
- Review the main result to see the greatest common divisor instantly.
- Use the supporting cards to compare the normalized values, reduced pair, and whether the numbers are coprime.
- Use Example to load a sample pair or Clear to reset both inputs.
GCD calculator examples
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GCD of 12 and 18
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greatest common factor of 36 and 60
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are 14 and 25 relatively prime
What this GCD calculator covers
This tool calculates the greatest common divisor, also called the greatest common factor (GCF) or highest common factor (HCF), for two whole numbers. It also shows the reduced pair after dividing by the GCD so you can see how much shared factor the two values contain.
When a GCD calculator is useful
A GCD calculator is useful when you need to reduce fractions, simplify integer relationships, prepare values for ratio work, or check whether two numbers are coprime. You can reduce fractions by dividing both values by the GCD, and you can simplify ratios using the GCD before rewriting the pair in lower terms. Instead of listing factors manually, you can enter the two numbers and get the largest shared factor instantly.
GCD vs LCM
The GCD is the largest factor that divides both numbers evenly. The least common multiple, or LCM, is the smallest multiple shared by both numbers. If your goal is to reduce or simplify, the GCD is usually the better starting point.
GCD calculator FAQs
What does GCD mean?
GCD means greatest common divisor. It is the largest whole number that divides both input values evenly.
Is GCD the same as GCF or HCF?
Yes. Greatest common divisor, greatest common factor, and highest common factor all refer to the same idea.
Can I use negative numbers?
Yes. The calculator accepts negative integers and normalizes them to absolute values before calculating the GCD.
Can I use 0 in the GCD calculator?
Yes. The calculator accepts 0 together with a non-zero whole number, so gcd(0, n) returns the absolute value of n. The only invalid zero case is 0 and 0 together, because that does not produce a defined GCD.