The number of multiples of a given number is finite.
Step 1: What is a multiple?
A multiple of a number is what you get when you multiply that number by a whole number.
For a number \(n\):
\(n \times 1\), \(n \times 2\), \(n \times 3\), \(\dots\)
Step 2: Whole numbers never end.
Whole numbers are \(1, 2, 3, 4, \dots\)
For any whole number \(k\), there is always a next one, \(k+1\).
Step 3: So multiples never end.
If \(n \times k\) is a multiple, then the next one is \(n \times (k+1)\).
We can keep doing this forever.
Example:
Take \(n = 6\). Multiples are:
\(6 \times 1 = 6\), \(6 \times 2 = 12\), \(6 \times 3 = 18\), \(\dots\)
There is no “last” multiple.
Conclusion:
The number of multiples of any given number is infinite (they go on without end).
So the statement is false.