Accelerating the pace of engineering and science

# Documentation Center

• Trial Software

# igcd

Greatest common divisor of integers and complex numbers with integer real and imaginary parts

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```igcd(i1, i2, …)
```

## Description

igcd(i1, i2, ...) computes the greatest common divisor of the integers i1, i2, …

igcd computes the greatest common nonnegative divisor of a sequence of integers. If an argument of igcd is a single integer number, the function returns the absolute value of that argument.

igcd also computes the greatest common divisor of a sequence of complex numbers of the domain DOM_COMPLEX. Both the real and the imaginary parts of all complex numbers in a sequence must be integers. The greatest common divisor is a complex number with a positive real part and a nonnegative imaginary part.

If all arguments are 0, igcd returns 0.

If there are no arguments, igcd also returns 0.

If one argument is a number, but is neither an integer nor a complex number with integer real and imaginary parts, then igcd returns an error message.

If at least one of the arguments is 1 or -1, igcd returns 1. Otherwise, if one argument is not a number, the igcd function returns a symbolic igcd call.

## Examples

### Example 1

Compute the greatest common divisor of the following integers:

`igcd(-10, 6), igcd(6, 10, 15)`

```a := 4420, 128, 8984, 488:
igcd(a), igcd(a, 64)```

### Example 2

Compute the greatest common divisor of the following complex numbers:

`igcd(-10*I, 6), igcd(10 - 5*I, 20 - 10*I, 30 - 15*I)`

### Example 3

The following example shows some special cases:

`igcd(), igcd(0), igcd(1), igcd(-1), igcd(2)`

### Example 4

If one argument is not a number, then the result is a symbolic igcd call. However, if at least one of the arguments is 1 or -1, the greatest common divisor is always 1:

```delete x:
igcd(a, x), igcd(1, x), igcd(-1, x)```

`type(igcd(a, x))`

## Parameters

 i1, i2, … arithmetical expressions representing integers or arithmetical expressions representing complex numbers of the domain DOM_COMPLEX, of which both the real part and the imaginary part are integers.

## Return Values

Nonnegative integer, a complex number both the real and imaginary parts of which are integers, or a symbolic igcd call.