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An online tool to calculate the greatest common divisor (GCD) of multiple integers. Supports space-separated number lists.
GCD(24, 36) = 12Overview
Understand what the tool solves, how it works, and the boundaries of its data.
The greatest common divisor (GCD), also called the greatest common factor (GCF), is the largest positive whole number that divides every number in a list with no remainder. This calculator accepts at least two positive integers separated by spaces, commas, or line breaks. It shows the numbers it recognized, the GCD, and an equation such as GCD(24, 36, 48) = 12.
A shared divisor is useful when reducing a fraction, simplifying a whole-number ratio, or splitting quantities into identical groups. The answer is determined entirely by the values you enter.
For two positive integers, the Euclidean algorithm replaces a pair with the smaller number and the remainder from dividing the larger by the smaller. The common divisors stay the same at each step. When the remainder reaches zero, the last nonzero divisor is the GCD.
GCD(a, b) = GCD(b, a mod b)
Example: 48 mod 18 = 12; 18 mod 12 = 6; 12 mod 6 = 0. Therefore GCD(48, 18) = 6.
With more inputs, the calculator combines the numbers successively: find the GCD of the first pair, then find the GCD of that result and the next number.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Separate values with spaces, commas, or new lines. For example, enter 84, 126, 210.
Compare the displayed number list with what you intended. The calculation uses the positive integer portions it recognizes, so stray text or decimal notation may not behave like a complete number.
The large result is the shared divisor; the equation summarizes the calculation. For 84, 126, and 210, the result is 42 because the quotients are 2, 3, and 5.
Use cases
See how the tool fits into real work and everyday tasks.
For 42/56, the GCD is 14. Dividing both terms by 14 gives 3/4, the reduced fraction.
If 84 notebooks and 126 pencils must be split into the greatest possible number of identical bundles with none left, the GCD is 42 bundles, each with 2 notebooks and 3 pencils.
The ratio 36:60:84 reduces to 3:5:7 after every term is divided by their common GCD, 12.
Q&A
Find concise answers to common questions and confusing cases.
For ordinary whole-number arithmetic, greatest common divisor and greatest common factor refer to the same largest shared positive divisor. “GCF” is common in U.S. classroom language.
It needs at least two recognized positive integers. Zero, negative values, and values that do not parse as positive integers are not included as supported inputs.
No. It means there is no positive common factor greater than 1 shared by the entire list. For example, 6, 10, and 15 have a list GCD of 1, although each pair shares a factor.
Notes
Review scope, result limitations, and important precautions before use.
Use positive integers written as plain digits. Decimal values, negative values, zero, units, and extremely large integers are outside the reliable input scope. Numeric precision is finite, so independently verify results involving very large values or work that requires exact arbitrary-precision arithmetic.
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