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Re: How many numbers between 1 and 100, inclusive, have exactly 5 positive [#permalink]
To find the number of factors a number has, we carry out prime factorisation, add one to the exponent of each of the prime factors and then multiply those figures. Against this background, we can only obtain 5 if there is only one prime factor and if that prime factor has 4 as its exponent. So, our focus will be on prime numbers that are raised to the power of 4 and which give numbers that are between the specified 1 to 100 range. Only 2 and 3 raised to the power of 4 satisfy this condition, giving numbers 16 and 81 respectively. The answer is thus option C.

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Re: How many numbers between 1 and 100, inclusive, have exactly 5 positive [#permalink]
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