The concept of "smooth number" is applied to all those numbers whose prime factors are lesser than or equal to 7: 60 is a smooth number (2 * 2 * 3 * 5), 111 is not (3 * 37).
More specifically, smooth numbers are classified by their highest prime factor and your are tasked with writing a isSmooth/is_smooth function that returns a string with this classification as it follows:
- 2-smooth numbers should be all defined as a
"power of 2", as they are merely that; - 3-smooth numbers are to return a result of
"3-smooth"; - 5-smooth numbers will be labelled as
"Hamming number"s; - 7-smooth numbers are classified as
"humble numbers"s; - for all the other numbers, just return
non-smooth.
Examples:
isSmooth(16) == "power of 2"
isSmooth(36) == "3-smooth"
isSmooth(60) == "Hamming number"
isSmooth(98) == "humble number"
isSmooth(111) == "non-smooth"
The provided input n is always going to be a positive number > 1.