They presented the problem:
Given that the number 8881 is not a prime number, prove by contradiction that it has a prime factor that is at most 89.
One of the answers was this:
If all prime factors where superior to 89, they would be at least 97. Counting them with their multiplicity, if there was only one such factor it would be 8881, which contradicts the given fact that 8881 is not prime. If there are at least two (possibly equal) factors a and b, then ab≤8881 but ab≥97∗97>8881, contradiction.
I understand it until
Counting them with their multiplicity, if there was only one such factor it would be 8881
What does it mean to count numbers with their multiplicity and in this case why would the only factor be 8881.
Moreover another answer states
You're on the right lines. If 8881 is not prime, it must have at least one prime factor not equal to itself. If it has no prime factors less than or equal to 89, then it must have only prime factors greater than or equal to 97, which is the next prime up from 89. You've already found the smallest natural number which has prime factors greater than or equal to 97 (in reference to the proposed solution to the question where they state that smallest number composed of only 97 is 97^2
However wouldn't the smallest natural number which has prime factors greater than or equal to 97 be 97?
Thank you and sorry if this seems like a stupid question.