igcd -- the greatest common divisor
of integers
Introductionigcd(i1, i2...) computes the greatest
common divisor of the integers i1, i2, ...
Call(s)igcd(i1, i2...)
Parametersi1, i2... |
- | arithmetical expressions representing integers |
Returnsa nonnegative integer, or a symbolic
igcd call.
Related
Functionscontent, div, divide, factor, gcd, gcdex, icontent, ifactor, igcdex, ilcm, lcm, mod
Detailsigcd computes the greatest common nonnegative divisor
of a sequence of integers. igcd
with a single numeric argument returns its absolute value.
igcd returns 0 when all arguments are
0 or no argument is given.igcd returns an error message if one argument is a number but not an integer. If at least one of the arguments is
1 or -1, then igcd returns
1. Otherwise, if one argument is not a number, then a symbolic igcd call is
returned.igcd is a function of the system kernel.
Example
1We compute the greatest common divisor of some integers:
>> igcd(-10, 6), igcd(6, 10, 15)
2, 1
>> a := 4420, 128, 8984, 488: igcd(a), igcd(a, 64)
4, 4
The next example shows some special cases:
>> igcd(), igcd(0), igcd(1), igcd(-1), igcd(2)
0, 0, 1, 1, 2
If one argument is not a number, then the result is a
symbolic igcd call, except in some special cases:
>> delete x: igcd(a, x), igcd(1, x), igcd(-1, x)
igcd(4420, 128, 8984, 488, x), 1, 1
>> type(igcd(a, x))
"igcd"
1 or -1, then
igcd returns 1.