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Euclidean Algorithm Trace Calculator — result sheet
Find the greatest common divisor of two whole numbers and show the successive division remainders.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Repeatedly replace (a,b) with (b, a mod b) until the remainder is zero; the final nonzero divisor is gcd(a,b).
The Euclidean algorithm reduces a pair of integers without changing their common divisors. The trace makes each quotient and remainder visible rather than returning only the final gcd.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First integer — Enter a signed whole number.
- Second integer — Enter a signed whole number.
Worked example
| Input | Value |
|---|---|
| First integer | 252 |
| Second integer | 105 |
gcd =21; trace: 252=2×105+42, 105=2×42+21, 42=2×21+0.
Assumptions and limits
- Inputs are signed whole numbers represented by decimal text.
- At least one input is nonzero.
- The result is a nonnegative greatest common divisor; least common multiples and modular inverses are not inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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