# divisors

Divisors of integer or expression

## Syntax

``divisors(n)``
``divisors(expr,vars)``

## Description

example

````divisors(n)` finds all nonnegative divisors of an integer `n`.```

example

````divisors(expr,vars)` finds the divisors of a polynomial expression `expr`. Here, `vars` are polynomial variables.```

## Examples

### Divisors of Integers

Find all nonnegative divisors of these integers.

Find the divisors of integers. You can use double precision numbers or numbers converted to symbolic objects. If you call `divisors` for a double-precision number, then it returns a vector of double-precision numbers.

`divisors(42)`
```ans = 1 2 3 6 7 14 21 42```

Find the divisors of negative integers. `divisors` returns nonnegative divisors for negative integers.

`divisors(-42)`
```ans = 1 2 3 6 7 14 21 42```

If you call `divisors` for a symbolic number, it returns a symbolic vector.

`divisors(sym(42))`
```ans = [ 1, 2, 3, 6, 7, 14, 21, 42]```

The only divisor of `0` is `0`.

`divisors(0)`
```ans = 0```

### Divisors of Univariate Polynomials

Find the divisors of univariate polynomial expressions.

Find the divisors of this univariate polynomial. You can specify the polynomial as a symbolic expression.

```syms x divisors(x^4 - 1, x)```
```ans = [ 1, x - 1, x + 1, (x - 1)*(x + 1), x^2 + 1, (x^2 + 1)*(x - 1),... (x^2 + 1)*(x + 1), (x^2 + 1)*(x - 1)*(x + 1)]```

You also can use a symbolic function to specify the polynomial.

```syms f(t) f(t) = t^5; divisors(f,t)```
```ans(t) = [ 1, t, t^2, t^3, t^4, t^5]```

When finding the divisors of a polynomial, `divisors` does not return the divisors of the constant factor.

```f(t) = 9*t^5; divisors(f,t)```
```ans(t) = [ 1, t, t^2, t^3, t^4, t^5]```

### Divisors of Multivariate Polynomials

Find the divisors of multivariate polynomial expressions.

Find the divisors of the multivariate polynomial expression. Suppose that `u` and `v` are variables, and `a` is a symbolic parameter. Specify the variables as a symbolic vector.

```syms a u v divisors(a*u^2*v^3, [u,v])```
```ans = [ 1, u, u^2, v, u*v, u^2*v, v^2, u*v^2, u^2*v^2, v^3, u*v^3, u^2*v^3]```

Now, suppose that this expression contains only one variable (for example, `v`), while `a` and `u` are symbolic parameters. Here, `divisors` treats the expression `a*u^2` as a constant and ignores it, returning only the divisors of `v^3`.

`divisors(a*u^2*v^3, v)`
```ans = [ 1, v, v^2, v^3]```

## Input Arguments

collapse all

Number for which to find the divisors, specified as a number or symbolic number.

Polynomial expression for which to find divisors, specified as a symbolic expression or symbolic function.

Polynomial variables, specified as a symbolic variable or a vector of symbolic variables.

## Tips

• `divisors(0)` returns `0`.

• `divisors(expr,vars)` does not return the divisors of the constant factor when finding the divisors of a polynomial.

• If you do not specify polynomial variables, `divisors` returns as many divisors as it can find, including the divisors of constant symbolic expressions. For example, `divisors(sym(pi)^2*x^2)` returns ```[ 1, pi, pi^2, x, pi*x, pi^2*x, x^2, pi*x^2, pi^2*x^2]``` while `divisors(sym(pi)^2*x^2, x)` returns ```[ 1, x, x^2]```.

• For rational numbers, `divisors` returns all divisors of the numerator divided by all divisors of the denominator. For example, `divisors(sym(9/8))` returns ```[ 1, 3, 9, 1/2, 3/2, 9/2, 1/4, 3/4, 9/4, 1/8, 3/8, 9/8]```.

## Version History

Introduced in R2014b