factorial

Factorial of input

Syntax

f = factorial(n)

Description

f = factorial(n) returns the product of all positive integers less than or equal to n, where n is a nonnegative integer value. If n is an array, then f contains the factorial of each value of n. The data type and size of f is the same as that of n.

The factorial of n is commonly written in math notation using the exclamation point character as n!. Note that n! is not a valid MATLAB^® syntax for calculating the factorial of n.

Examples

10!

f = factorial(10)

f = 
3628800

22!

format long
f = factorial(22)

f = 
     1.124000727777608e+21

In this case, f is accurate up to 15 digits, 1.12400072777760e+21, because double-precision numbers are only accurate up to 15 digits.

Reset the output format to the default.

format

Factorial of Array Elements

n = [0 1 2; 3 4 5];
f = factorial(n)

f = 2×3

     1     1     2
     6    24   120

Factorial of Unsigned Integer Values

n = uint64([5 10 15 20]);
f = factorial(n)

f = 1×4 uint64 row vector

                   120               3628800         1307674368000   2432902008176640000

Input Arguments

n — Input values

scalar, vector, or array of real, nonnegative integer values

Input values, specified as a scalar, vector, or array of real, nonnegative integers.

Example: 5

Example: [0 1 2 3 4]

Example: int16([10 15 20])

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Tips

Limitations

• For double-precision inputs, the result is exact when n is less than or equal to 21. Larger values of n produce a result that has the correct order of magnitude and is accurate for the first 15 digits. This is because double-precision numbers are only accurate up to 15 digits.

• For single-precision inputs, the result is exact when n is less than or equal to 13. Larger values of n produce a result that has the correct order of magnitude and is accurate for the first 8 digits. This is because single-precision numbers are only accurate up to 8 digits.

Saturation

• The table below describes the saturation behavior of each data type when used with the factorial function. The values in the last column indicate the saturation point; that is, the first positive integer whose actual factorial is larger than the maximum representable value in the middle column. For single and double, all values larger than the maximum value are returned as Inf. For the integer data types, the saturation value is equal to the maximum value in the middle column.

  Data type	Maximum Value	Factorial Saturation Threshold
  double	realmax	factorial(171)
  single	realmax('single')	factorial(single(35))
  uint64	264-1	factorial(uint64(21))
  int64	263-1	factorial(int64(21))
  uint32	232-1	factorial(uint32(13))
  int32	231-1	factorial(int32(13))
  uint16	216-1	factorial(uint16(9))
  int16	215-1	factorial(int16(8))
  uint8	28-1	factorial(uint8(6))
  int8	27-1	factorial(int8(6))

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The factorial function supports GPU array input with these usage notes and limitations:

• 64-bit integers are not supported.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Usage notes and limitations:

• 64-bit integers are not supported.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a