Yes.
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Yes, negative 7168 divisible by 2; it is negative 3584.
no.. for example 6,12,18 are divisible by 2..but not divisible by 8.
Yes. 8 / 4 = 2 8 is also divisible by 2 and 8.
Being divisible by 4, means that it will also be divisible by 2, so that doesn't tell you anything about divisibility by 8. But if you divide the number by 2, and this quotient is divisible by 4, then yes the original number is divisible by 8.
No. If it is not divisible by 2 it cannot be divisible by 8, so don'y bother.