LaTeX
\gcd(a,b)=\gcd(b,a\bmod b)Variables
- a,b: integers
- mod: remainder operation
How to use this formula
Computes a greatest common divisor by repeated remainders.
Important notes
- The displayed recurrence is applied until the remainder is zero.
Quick example
gcd(48,18)=6.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The displayed recurrence is applied until the remainder is zero.
- Apply the formula over the intended integer domain and check divisibility, coprimality, parity, or modulus conditions.
Worked example
gcd(48,18)=6.
Common mistakes
- Before substituting values into Euclidean Algorithm, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Verify the result of Euclidean Algorithm with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Euclidean Algorithm in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\gcd(a,b)=\gcd(b,a\bmod b). - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Euclidean Algorithm used for?
Computes a greatest common divisor by repeated remainders.
Can I copy this formula as LaTeX?
Yes. Copy \gcd(a,b)=\gcd(b,a\bmod b) or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.