If they had asked for "the number of factors which are multiples of 8
but not a multiple of 25", there are some theorems we could use.
. . . There are 12.
But they asked for the sum of these factors.
I see no choice but to find all these factors and add them.
It is not a very intellectual problem, is it?
There are 60 factors.Find the sum of the factors of 18,000 which are multiple of 8 but are not multiple of 25.
I found them by simple division.
. . . . . . . .
As promised, there are 12 such factors.
Their sum is: .