I thought about this for a while and then recognized that this number is possibly divisible by {3, 4, 6, 8, 9, 10, 12, etc.}
So I look for possible sets of 3 numbers here that add up to 18. The first such set I recognized was {4, 6, 8}. These digits do add up to 18. Unfortunately, 468 is not in the desired range (600,700).
Thus, I could try either {6, 4, 8} or {6, 8, 4}.
There may be other combinations of 3 numbers (which must add up to 18).
Test 684. Is 684 between 600 and 700, not including 600 or 700? YES.
Is the sum of {6, 4, 8} equal to 18? YES. So, 648 is one possible answer. Are there others?
