SolutionThis question is really tricky. It could be daunting if you do not use the right strategy

What we do know is that 25 factorial \(25!\) is equal to \(25*24*23*22.........*1\) inclusive. Now every number that is in between this range is a factor of \(25!\) and every number outside this range but is the result of a multiplication of two numbers of the range, then is also a factor of \(25!.\)

To give an example: choice A is 26 and this is \(2*13\); these two numbers are both factors of \(25!.\) Looking at the answer choices, we do notice that choice E 58 is the result of \(2*29\).

2 is a factor of \(25 !\) but 29 it is not.

Be careful reading the question: all the answer choice but E are prime factors or simply factors in between the range. E has a prime in but 29 is out. So is the only possible answer

The answer is \(E\)

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