What is the biggest number that always divides the product of three co

Question

What is the biggest number that always divides the product of any three consecutive Integers? A) 2 B) 3 C) 6 D) 12 E) 24 Source: https://www.GMATinsight.com

seevikrant · Answer

B. 3 will 'always' divide the prod of any 3 cons integers. It is the only hence the biggest such no.

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pratykank · Answer

The answer should be 'C'.

Three consecutive numbers -> x(x+1)(x+2)
will always have one number divisible by 2 and one number divisible by 3

So the product will be a multiple of 2*3 =6

BrentGMATPrepNow · Answer

There's a nice rule says:   The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1  
So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1
Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, 2 and 1
NOTE: the product may be divisible by other numbers as well, but these divisors are guaranteed.

So, we can be certain that the product of any three consecutive integers will be divisible by 3 and by 2, which means any three consecutive integers will ALWAYS be divisible by 6

Answer:  C

Cheers,
Brent

JeffTargetTestPrep · Answer

We may recall the rule that the product of n consecutive integers is divisible by n!. Thus, the product of 3 consecutive integers is divisible by 3! = 6.
 
If you don’t recall the rule, consider the three consecutive integers 1, 2, 3: their product is 1 x 2 x 3 = 6. Now test the answer choices. The product 6 is divisible by 2, 3, and 6. The greatest of these is 6. 
 
Answer: C

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What is the biggest number that always divides the product of three co

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What is the biggest number that always divides the product of three co

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