For how many integer values of \(n\) between 1 and 474 inclusive does the decimal representation of \(\frac{n}{475}\) terminate?
19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380 399 418 437 456 Total = 24 such integers.
Note: ALL of them are multiples of 19
Hint: Try prime factorizing 475. What is the number without a power? Then, find all of the multiples of [insert number in 475's prime factorization without a power here] from 1 to 474.