Built-in Mathematica Symbol

GCD

GCD[n₁, n₂, ...]
gives the greatest common divisor of the n_i.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

GCD works not only with integers but also rational numbers, both real and complex.

For rational numbers r_i, GCD[r₁, r₂, ...] gives the greatest rational number r for which all the r_i/r are integers.

Greatest common divisor of three numbers:

Plot the GCD for a number with 1000:

Greatest common divisor of three numbers:

Plot the GCD for a number with 1000:

GCD threads element-wise over lists:

Use with rational arguments:

Use with Gaussian integers:

Find the fraction of pairs of the first 100 numbers that are relatively prime:

The result is close to

:

Plot the means of the GCDs for successive "balls" of numbers:

Conditions for solvability of a linear congruence equation:

GCDs of Fibonacci numbers:

Use CoprimeQ to check for trivial GCDs:

Compute GCD from Floor:

Use in sums:

Simplify expressions containing GCD:

Reduce inequalities involving GCD:

GCD is very fast, even for many very large integers:

Signs are discarded:

The arguments must be explicit integers:

GCD sorts its arguments:

Plot the argument of the Fourier transform of the GCDs:

Form GCDs of 1 with rational numbers:

A GCD property of Fibonacci numbers: