Q: Every multiple of a non-zero number is greater than the number?

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It has to be a whole number, or else every number would be a multiple of every other number.

Because your beginning number was a multiple of 2.

Every number greater than 1 has the two factors 1 and the number itself.

no

Every multiple of any number (except 0 or 1) is composite.

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Every nonzero number has multiples. Every set of nonzero numbers has an LCM.

Not with negative numbers. -10 is a multiple of -2.

Yes! it is.

It is the number itself.

Because every one of then is a multiple of 2.

Every nonzero whole number can be factored.

Not all (5 is prime) but every multiple of 5 greater than 5 is composite because they have more than two factors. Every multiple of any integer greater than one is composite.

Every nonzero number is a factor of itself.

This is true.

The LCf of any two nonzero whole numbers is one because every nonzero whole number can be divided by it.

Because if they were even they would be a multiple of 2 and thus not prime.

No. A notable exception is the set of prime numbers.