Question 1102800: The product of how many consequtive intgers must be divisible by 5040?
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
7.
5040 is 7! = 7*6*5*4*3*2*1.
In any 7 consecutive integers, there will always be at least one of them divisible by 2, at least one divisible by 3, ..., at least one divisible by 6, and exactly one divisible by 7.
So the product of any 7 consecutive integers will contain at least one factor each of the numbers 2 through 7; that means the product will be divisible by 7!=5040.
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