Factorion
Other bases
If the definition is extended to include other bases, there are an infinite number of factorions. To see this, note that for any integer n > 3 the numbers n!

Factorion

Section Title: Other bases
Table Section Text: If the definition is extended to include other bases, there are an infinite number of factorions. To see this, note that for any integer n > 3 the numbers n!

Base n	Factorion expressed in base n	Factorion expressed in base 10

1	1, 11, 111, ...	1, 2, 3, ... (all integers ≥1)

≥1	1	1 = 1!

2	10	2 = 2!

≥3	2	2 = 2!

4	13	7 = 1! + 3!

5	144	49 = 1! + 4! + 4!

6	41	25 = 4! + 1!

42	26 = 4! + 2!

9	6 2558	41,282 = 6! + 2! + 5! + 5! + 8!

10	145	145 = 1! + 4! + 5!

4 0585	40,585 = 4! + 0! + 5! + 8! + 5!

Sentence(s)

145 is a factorion because 1! + 4! + 5! = 145.

final_sentence: 145 is a factorion because 1! + 4! + 5! = 145.