There are 24 number made by permutations of the digits. There are lots more if the digits can be repeated, for example, 27335722. Even more can be made by using arithmetic and algebraic operations, for example 35^27 = approx 4.8960*10^41. You have not specified what the rules for "making" numbers are!
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All numbers are made with digits and there is no limit on how big they can be. So there is no greatest number.
Assuming you mean permutations of three digits, then the set of numbers that can be made with these digits is: 345 354 435 453 534 543 There are six possible permutations of three numbers.
You can make 24 numbers by rearranging the digits. However, you can make vastly more if you allow mathematical operations on the digits. For example, 3+5*8-6 = 37.
Armstrong numbers are the sum of their own digits to the power of the number of digits.
Digits are numbers.