Find the smallest number by which 8789 must be divided so that the quotient is a perfect cube.
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8789 = 11 * 799
= 11 * 17 * 47
8789 = n * q³ + r
we want the smallest number n that means we want the largest value for q³.
20³ = 8000
21³ = 8000+1+1200+60 = 9261 > 8789
so q must be 20.
8789 = 1 * 20³ + 789 or 1 * 8000 + 789
The answer is 1.
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If we want an answer other than 1, then
8789 = 2³ * 10³ + 789
so smallest number in this case = 2³ = 8
= 11 * 17 * 47
8789 = n * q³ + r
we want the smallest number n that means we want the largest value for q³.
20³ = 8000
21³ = 8000+1+1200+60 = 9261 > 8789
so q must be 20.
8789 = 1 * 20³ + 789 or 1 * 8000 + 789
The answer is 1.
====
If we want an answer other than 1, then
8789 = 2³ * 10³ + 789
so smallest number in this case = 2³ = 8
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