If r,s and t are consecutive positive multiples of 3....

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3rd ed. Number properties ch.4 p.87 #9

If r,s and t are consecutive positive multiples of 3. Is rst divisible by 27, 54, or both?

The answer currently states that the product of rst must have 3 3’s as factors and at least one 2. I agree, but wouldn’t the product also contain a fourth 3, because this is a set of 3 consecutive integers?

Thanks,

Tom

[StaceyKoprince]

Nice! Yes, you can say that three consecutive multiples of 3 must contain four 3's as factors. Two of the three consecutive numbers will contain at least one multiple of 3. One of the three consecutive numbers must also be a multiple of 9 (which occurs every 3rd multiple of 3), so that number will contribute at least two 3's as factors.

I assume that the explanation doesn't point this out because we don't need that info to solve - but it would be nice if the explanation mentioned it anyway! :)

It's great that you noticed this extra info - because this might come into play on an even harder question!