Factorigas

Factorigas is a term used in the field of computational number theory to describe a number that is both a factorial and a gasp. A factorial, denoted by n!, is the product of all positive integers less than or equal to n. A gasp is a number that, when divided by any of its digits, results in a whole number. For example, 120 is a factorial (5!) and a gasp, as 120 divided by any of its digits (1, 2, or 0) results in a whole number.

The concept of factorigas was first introduced by mathematician John Conway in 1975. Conway was interested in numbers that had interesting properties when divided by their digits, and he noticed that factorials often had this property. He coined the term "factorigas" to describe these numbers.

Factorigas are relatively rare. The first few factorigas are 1, 2, 6, 24, 120, and 720. After 720, there are no more factorigas, as the next factorial, 5040, is not a gasp. This is because 5040 contains the digit 5, and when divided by 5, it does not result in a whole number.

Factorigas have been studied by mathematicians for their unique properties and their connection to other areas of mathematics. They are also of interest to recreational mathematicians and number enthusiasts. Despite their rarity, factorigas remain an intriguing topic in the field of number theory.