800
400,2
200,2,2
100,2,2,2
50,2,2,2,2
25,2,2,2,2,2
5,5,2,2,2,2,2
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400 is the smallest multiple of 100 that has 8 as a factor.
longest string for 800 =2*2*2*2*2*5*5
Contractor , shatter , batter , chatter , factor, ladder , sadder, compactor, , clatter , matter , fatter , tractor,bladder ,madder.
800 + 800 + 800 + 800 + 800 = 4,000
It is: 800