Question 994377: What is that number , when that number is divided by 9 the remainder is 8 , when that number is divided by 8 the remainder is 7 , when that number is divided by 6 the remainder is 5 , when that number is divided by 5 the remainder is 4 , when that number is divided by 4 the remainder is 3 , when that number is divided by 3 the remainder is 2 , when that number is divided by 2 the remainder is 1
Answer by AnlytcPhil(1806)   (Show Source):
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We use the fact that if p is a factor of n then when n-m (0 <= m <= n)
is divided by p < n-m, the remainder is p-m.
The required remainders are all 1 less than the required
divisors respectively, so in this case m=1. We take the
LCM of 9,8,6,5, and 4 which is 360 and subtract 1. Since
360 is a multiple of each of those, the remainders when
1 less that 360 or 359 is divided by them will be 1 less
than them.
Answer: 359
Checking
39 44 59 71 89
9)359 8)359 6)359 5)359 4)359
27 32 30 35 32
89 39 59 9 39
81 32 54 5 36
8 7 5 4 3
Edwin
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