Manhattan GMAT Math Question (Ch 4 Consecutive Integers)

the rule is that the product of n numbers of consecutive integers is always multiple of n. So for your question, product of 3 consecutive numbers will be multiple of 3. So the product is multiple of any product of 2,3,2 and 2.

Thanks for the response!

So, it means that the rule applies not only to consecutive integers but any evenly spaced set?

That is correct. For example, 2*4*6 = 48

The factors to this are...1,2,3,4,6,8,12,16,24,48.

The guaranteed ones will always be 1,2,3,4,6,8 based on the number properties rules of 3 even consecutive integers.

Ah. I get it now. Thank you all very much!

List at least six factors of the product of 3 consecutive even integers?

Why are 5 & 7 not factors

Ex. 10, 12, 14

Prime Factors

10 - (5,2)
12 - (3,2,2)
14 - (7,2)

Thanks for you assistance!

5 and 7 will not be factors in every group of 3 even consecutive integers. e.g. 2, 4, and 6
Are 5 and 7 factors here? No!
We need to give only those factors which are definitely (in every case) factors of the product of 3 consecutive even integers.

Since the 3 numbers are even, we will get three 2s as factors. Let's say we take the three 2s out: 2*4*6 = 2*2*2(1*2*3)
Now we just have 3 consecutive integers and three 2s. In the product of any three consecutive integers, 1, 2, 3 and 6 are definitely factors. (For this theory, check out the below given posts.)
This means, the product of 3 consecutive integers will definitely have 2*2*2*6 = 48 as a factor. So all the factors of 48 will definitely be factors of the product of three even consecutive integers.

I have chosen 3 even consecutive integers 10, 12, 14
Product of 10x12x14 = 1680

List of factors of 1680 are 1,2,3,4,5,6,7,8,210,240,280,336,420...
From list we can consider any 6 factors of product.

Is my strategy right?
Thanks.

No. The question is
"List at least six factors of the product of 3 consecutive even integers?"

The 3 consecutive even integers could be any 3 consecutive integers. For every such triplet, the six factors should be common.

If you take the numbers as 2, 4 and 6, the 6 factors should be factors of their product too. So any 6 factors from your list above will not work. They need to be the 6 factors that are common to the product of any valid triplet.

Look at the explanation given here: manhattan-gmat-math-question-ch-4-consecutive-integers-118800.html#p987784

List at least six factors of the product of 3 consecutive even integers.

I am unable to follow the explanation in MGMAT..kindly help me understand this problem.

Thanks in advance!

Please check above.