Hi Greg,
I was watching Arithmetic Section 3, last question about integers less than 100 having 4 factors.
Can you explain why didn’t we consider 9, 25 and 49 in the answers? I think they should be counted because the question didn’t mention 4 unique factors.
Please help.
Thank you.
9 only has three factors - 1, 3 and 9. You cannot “double-count” identical numbers, as otherwise you could claim that every integer has infinite factors.
Hi, thank you for the revert.
Can you further explain how does the infinite factor thing work? The product of two factors should always add up to give the number right? How are infinite factors possible then?
If you consider identical factors as the same, one could argue that (for instance) 1 has infinite factors of 1. That indeed can’t be the case.
Noted.
That’s the only case, right?
Not sure on what you mean.
You said that every integer can have infinite factors; but how is this true in respect to this question? Are there any examples other than 1?
That is not what I was saying. I was explaining why
Can you explain why didn’t we consider 9, 25 and 49 in the answers? I think they should be counted because the question didn’t mention 4 unique factors.
was the case. You claimed that the question wasn’t asking for unique factors, and hence I said that meant that you would have duplicate factors - in other words, when a question is asking about “factors”, they mean only unique ones. To be clear,
is not true, and is why “why didn’t we consider 9, 25 and 49 in the answers”.
