Reference · Math

math.factorial

math.factorial(int) -> int

What it does

n!, the product of the ints from 1 to n, as an int, as Python's math.factorial. math.factorial(0) is 1. Quillo's ints are 64 bits and there is no bigint, so the largest factorial that fits is 20!; Python's grows without bound.

Examples

print(math.factorial(0), math.factorial(1), math.factorial(5))print(math.factorial(20))print(math.factorial(10) / (math.factorial(3) * math.factorial(7)))

1 1 1202432902008176640000120

Edge cases

• 21! does not fit in an int: it is a runtime error, integer overflow, not a float and not a wrapped value, in the browser as on the server, where 20! is exact too, past 2^53. For the size of a large factorial use math.lgamma (lgamma(n + 1) is log(n!)), or math.gamma up to 170! as a float.
• A float that is a whole number is accepted: math.factorial(5.0) is 120. A float with a fraction is not.
• math.comb and math.perm count without computing the full factorials, so they reach further than n! itself does.

print(math.factorial(5.0), math.gamma(21), math.lgamma(21))print(math.comb(30, 15))

120 2432902008176640000 42.335616460753485155117520

print(math.factorial(21))

line 1: integer overflow

Errors

A negative number is a runtime error, not an error value, with a message that says so; Python raises ValueError there too. A fraction, text or null is a runtime error as well.

print(math.factorial(-1))

line 1: `math.factorial` is not defined for negative numbers (-1)

print(math.factorial(5.5))

line 1: `math.factorial` expects an int as argument 1, got float

Chaining

In a pipeline the number comes first:

print(5 | math.factorial)print(range(0, 6) | map(math.factorial))

120[1, 1, 2, 6, 24, 120]

See also

math.gamma, math.lgamma, math.comb, math.perm, math.prod

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