Question 1064533
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Find the greatest 4 digit number that has exactly 3 factors.
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<pre>
If the number has exactly 3 factors, it means that the number is the square of a prime number: N = {{{p^2}}}.

Then it has the factors 1 (one), p and {{{p^2}}}.


Indeed, if the number is a prime number, it has only TWO factors: 1 (one) and itself.

If the number is not prime and is not the square of a prime, then it has more than 3 factors.


Therefore, to answer the problem's question, we must take the square of the largest two-digit prime number, which is {{{97^2}}} = 9409.


<U>Answer</U>. The number under the question is 9409.
</pre>

Solved.



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You will spend TOO MUCH your valuable time by checking every number from 9999 down.


So, by giving this solution, I saved a lot of your time.