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No. All multiples of an even number are even. Here is why:
An even number is one that is a multiple of 2. Thus, it can be written in the form:
2n
where "n" is any integer. If you multiply this by another integer, call it "m", you get:
2n x m = 2mn
Since the product of two integers (m x n) is an integer, it follows that the result has a factor of 2 - i.e., it is even.
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Is 39 divisible by 6?
No. 39 is odd but 6 is even and all multiples of 6 are even.
Is 129 divisible by 6?
No. All multiples of 6 are even and 129 is odd so it cannot be divisible by 6.
What factors produce only odd multiples?
No number will produce only odd multiples, as any multiple of an even number will always be even. Proofs can be easily created of such a fact.
Are 123 and 6 multiples of 6?
123 is not a multiple of 6 but 6 is. When an even whole number is multiplied by any other whole number the result is always an even number. 6 is an even number, 123 is an odd numbers; therefore 123 cannot be a multiple of 6. 6 = 6 × 1; therefore 6 is a multiples of 6.
Why aren't all odd numbers divisible by 3?
Because not all odd numbers are multiples of 3 - I have shown you below that this is the case and you can see some multiples of 3 are even and some are odd and you can also see that there are even and odd numbers BETWEEN the multiples of 3. 1 (odd) 2 (even) 1*3 =3 (odd) 4 (even) 5 (odd) 2*3 = 6 (even) 7 (odd) 8 (even) 3*3 = 9 (odd) 10 (even) 11 (odd) 4*3 = 12 (even)
