### Instruction: When 19 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
Answer Choices: (A) 1 (B) 2 (C) 3 (D) 4 (E) 5.### Response: Let's reason about the multi-choice question.
This means that 16 must be a multiple of k.
The factors of 16 are 1, 2, 4, 8, and 16.
Out of these, k can be 4, 8, and 16.
The answer is C.