FoM CH.2 - Divisibility Drill 9

[EdwardL946]

Hello,

I have a question on the wording of problem 35 (drill 9) at the end of Chapter 2: Divisibility in Foundations of Math.

It states:
35. If 64 divides evenly into n, what are all of the known divisors of n?

Answer:
1, 2, 4, 8, 16, 32, 64: If 64 divides evenly into n, then any divisors of 64 will also be divisors of n.

Now, I know that "divisor" is another way to say "factor" but my issue came with the phrase at the start of the question. If 64 divides evenly into n - how can I understand that statement? Does that mean that when fully divided (e.g. fully factored) that all of the factors for 64 fit into the number n? And perhaps my greater question would be - will there ever be a case where n is not the same number as stated, but something else? The "divides evenly" part really threw me here and I had no idea what to think!

Thanks,
Edward

[Sage Pearce-Higgins]

Sure, that funny wording is perhaps a good takeaway from this problem. However, 'divides evenly' is simply another way of saying 'divides without a remainder' or 'is a factor'. Sometimes you might need to guess the meaning of a phrase like that to make sense of a problem.

will there ever be a case where n is not the same number as stated, but something else?

Certainly, I can say that 10 divides evenly into 10, but 10 divides evenly into 20 or 30 as well.