Recursive CTEs in SQL Server execute involving a temp table. This is probably why this tiny amount of work even takes a measurable amount of time. This should take <= 1ms.
Use a numbers table. Or, use one of the many tricks to materialize a sequence of numbers without table access such as:
FROM (VALUES (1), (2), ...) x(Num)
Number % 15 = 0 instead of
Number % 3 = 0 AND Number % 5 = 0 is less clear. It requires mathematical insight to convince anyone that this is even correct. Code should be obviously correct.
The default length of
varchar is unclear. (Can you tell from memory?!) Better use
nvarchar(400). By default, use Unicode characters in order to just never have certain bugs and problems.
These issues aside this query is simple. Anyone can very quickly understand it and conclude that it is correct. That's good code.