One reason is this counter-example:
20 is not divisible by 8 yet it's divisible by by both 4 and 2.
Also, if a number is divisible by 4, it's automatically divisible by 2, so
there would be no need to say that it's divisible by 2.
The sum of two multiples of 8 is also a multiple of 8.
Since 1000 is divisible by 8, then any number that ends in 000 is a multiple
of 1000 and is divisible by 8. So if the number formed by the last three
digits is a multiple of 8 then the number is divisible by 8, because it's
the sum of two multiples of 8.
For example, 17216. The last three digits are 216 and it is divisible by 8.
Thus, 17216 is divisible by 8. (That's because it's 17000+216 and both 17000
and 216 are divisible by 8.)
Edwin
