How to use the FACT() function in Excel

This function calculates the factorial of a specified non-negative integer.

Syntax
FACT(number)

Argument

• number (required) – A non-negative integer (decimal values are truncated)

Key Properties:

• For any positive integer n:
  n! = n × (n-1) × (n-2) × … × 2 × 1
• By definition: 0! = 1
• Maximum computable value in Excel: FACT(170) ≈ 7.26E+306
  (Larger values return #NUM! error)

Mathematical Background
Factorials represent:

• Permutations of distinct items
• Partial products of natural numbers
• Fundamental in combinatorics and probability

Example Applications:

1. Race Placement (Permutations)

=FACT(4) → Returns 24

Interpretation: 4 runners can finish in 24 different orders

1. Committee Arrangements

=FACT(5)/FACT(3) → Returns 20 (5P2 permutations)

1. Special Cases:

Error Conditions:

• #VALUE! – Non-numeric input
• #NUM! – Negative numbers or n > 170