Show that product of three consecutive integers is always divisble by 6.

Asked by  | 20th Apr, 2008, 06:21: PM

Expert Answer:

Hi Aks,

If a number is divisible by 2 and 3 both then the number is divisible by 6.

Every alternate number is an even number and is hence a multiple of 2. Thus out of 3 consecutive numbers atleast one is divisible by 2.

Also every third number is divisible by 3. Thus out of three consecutive numbers there is one and only one number that is a multiple of 3.

Thus out of 3 consecutive numbers there is atleast one multiple each of 2 and 3.

Thus the prodict of three consecutive numbers is always a multiple of 6.

Topper Learning Team

 

 

Answered by  | 12th Jun, 2008, 04:49: PM

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