Yes, each number does have an infinite number of multiples.
Here's why:
Multiples of a number are obtained by multiplying that number by any integer. Since the set of integers is infinite, the set of multiples will also be infinite.
Explanation:
A multiple of a number is the result of multiplying that number by an integer (whole number). For instance:
- Multiples of 2: 2, 4, 6, 8, 10, ...
- Multiples of 5: 5, 10, 15, 20, 25, ...
- Multiples of 10: 10, 20, 30, 40, 50, ...
Because you can continue multiplying any given number by increasing integers indefinitely, you will always be able to find another multiple. The natural numbers (1, 2, 3...) continue infinitely, which means that for any given number, you can always find an infinite number of multiples.
Example:
Let's take the number 7. We can multiply it by any positive integer:
- 7 x 1 = 7
- 7 x 2 = 14
- 7 x 3 = 21
- 7 x 4 = 28
- ...and so on.
As you continue to multiply 7 by larger and larger integers, the multiples keep increasing without end, illustrating the infinite nature of multiples.
Conclusion:
Therefore, given the infinite nature of integers, every number possesses an infinite number of multiples.
