Coprime Checker

About this calculator

Two whole numbers are coprime, or relatively prime, if the only positive integer that divides both of them evenly is 1 — their greatest common divisor (GCD) equals 1, even though neither number individually needs to be prime. This calculator finds that GCD using the Euclidean algorithm, one of the oldest algorithms in mathematics, which repeatedly replaces the larger number with the remainder of dividing it by the smaller until the remainder reaches zero.

Coprimality is a load-bearing concept well beyond number theory homework: RSA public-key cryptography requires choosing an encryption exponent that is coprime with a totient value to guarantee the encryption is mathematically invertible, gear designers deliberately choose coprime tooth counts for meshing gears to spread wear evenly across all tooth combinations rather than repeating the same pairs, and coprime denominators are what let fractions be added by finding a true least common denominator.

Enter two whole numbers and this calculator returns their GCD via the Euclidean algorithm and states whether they are coprime.