# Eduardo thinks of a number between 1 and 20 that has exactly 5 factors. What number is he thinking of?

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Answer is

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It is apparent that a number cannot be a prime number, if it has exactly

As a product of two prime numbers say

Now for remaining

Hence answer is

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The most direct method of finding the number that has

This is because factors are always in pairs, but in a square, one of the factors is multiplied by itself and it is only counted once. (the square root)

This means that of all the numbers from

It would seem that the largest one is most likely to have

Factors of

As a check, let's consider the other squares:

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