# Largest factor of consecutive natural numbers

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• Aug 5th 2013, 11:45 PM
rushabhjain1
Largest factor of consecutive natural numbers
1) The largest Number, which exactly divides the product of any three consecutive integers is ...

(a) 2 (b) 3 (c) 6 (d) 12
• Aug 6th 2013, 08:35 AM
ebaines
Re: Largest factor of consecutive natural numbers
Think about it ... for any three consecutive positive integers at least one must be even, and at least one must be a multiple of 3. What does that tell you about the largest number that must be divisible into the product of three consecutive positive integers?
• Aug 6th 2013, 08:47 AM
HallsofIvy
Re: Largest factor of consecutive natural numbers
One "product of three consecutive integers" is 1(2)(3). Another is 2(3)(4). What is the largest integer that divides both of those.
Of course, it remains to be shown that this integer divides any factor of three consecutive integers. What is true of every other integer? What is true of every third integer?