Coprime Checker

How it is calculated

The tool finds the greatest common divisor with the Euclidean algorithm: set x = a, y = b, then repeat (x, y) → (y, x mod y) until y = 0; the last x is gcd(a, b). The two numbers are coprime exactly when that gcd is 1, and the tool reports the gcd together with a Yes/No answer (Yes = coprime). Both inputs must be whole numbers of at least 1; decimals such as 12.5, zero and negatives return no result. Digit strings are read exactly, so integers up to 9,223,372,036,854,775,807 (the 64-bit limit) give an exact gcd; anything larger gives no result. Remember that coprime does not mean prime: 8 and 15 are coprime although neither is prime, while 7 and 14 are not coprime although 7 is prime.

Common mistakes

• Assuming coprime means both numbers are prime. Only the gcd matters: 9 and 16 are coprime, 3 and 9 are not.
• Thinking that consecutive numbers might share a factor. Any two consecutive whole numbers are always coprime, so a gcd of 1 is the expected result.
• Reading the Yes/No answer as the gcd. The answer shows only Yes or No; the gcd is the separate first output.
• Entering 0, a negative number or a decimal. Only positive whole numbers are accepted, so turn a fraction's numerator and denominator into integers first.
• Pasting a number with more than 19 digits, such as a long key or factorial. Above the 64-bit limit the tool shows no result instead of an approximate gcd.