Let's start with rule: if a number is a factor of y and a factor of x, it's also a factor of y+x.
if a number, let's say z, is a factor of x and y, we can say:
x = nz and y = mz , where n and z are integers.
Then x + y = nz + mz = (n+m)z ---> (n+m) is an integer and z is a factor of (n+m).
Now let's consider your example: if 8 is not a factor of g, is 8 a factor of 2g?
we can't apply the rule because 8 is not a factor. See examples,
1) g = 9: 8 is not a factor of g and not a factor of 2g (18).
2) g = 12: 8 is not a factor of g but is a factor of 2g (24 = 3*8)
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