The correct answer is option C) infinite.

Explanation:
To understand why the number of multiples of a given number is infinite, let's first define what a multiple is.

A multiple of a given number is any number that can be obtained by multiplying the given number by another integer. For example, the multiples of 3 are 3, 6, 9, 12, 15, 18, and so on.

To prove that the number of multiples of a given number is infinite, we can use the following reasoning:

1. Multiples are generated by multiplying the given number by different integers:
- For example, if the given number is 3, we can generate multiples by multiplying it by 1, 2, 3, 4, and so on.

2. There are an infinite number of integers:
- Integers are whole numbers, including positive numbers, negative numbers, and zero.
- We can always find another integer to multiply the given number by.

3. Therefore, the number of multiples of a given number is infinite:
- Since there is an infinite number of integers, we can always find another integer to generate a new multiple.

For example, let's consider the number 5. The multiples of 5 are 5, 10, 15, 20, 25, 30, and so on. As long as we continue to multiply 5 by different integers, we will generate an infinite number of multiples.

Hence, the correct answer is option C) infinite, as there is no limit to the number of multiples that can be generated for a given number.

Multiples of a number are the numbers exactly divisible by that number..ex multiples of 2 are 2n...and nis infinite