88 has exactly eight factors (1, 2, 4, 8, 11, 22, 44 & 88)
100.....1,2,4,5,10,20,25,50,100
The square of any prime number has exactly three factors: 22, 32, 52, etc.
1 is the only number between 1 and 100 that has too few factors to be a prime number.
65
In that range, only 100 has exactly 9 factors.
81 has 5 factors: 9x9 3 x 27 1 x 81
100.....1,2,4,5,10,20,25,50,100
The square of any prime number has exactly three factors: 22, 32, 52, etc.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
The numbers with exactly six factors between 1 and 100 are those that are perfect squares. Perfect squares have an odd number of factors because they have one factor that is repeated (the square root of the number). The factors of a number come in pairs, except for perfect squares. In this case, the factors are 1, the square root of the number, and the number itself. Examples of numbers with exactly six factors between 1 and 100 are 4, 9, 25, and 49.
To have an odd number of factors, the number must be a square. The only squares between 80 and 100 ()inclusive) are 81 and 100 but 81 does not have a factor of 5, and 100 has 9 factors. Thus the problem (as stated) has no solution. The numbers which have a factor of 5 must end in 0 or 5; the only numbers between 80 and 100 (inclusive) which match this criteria are {80, 85, 90, 95, 100}, which have {10, 4, 12, 4, 9} respectively. If you meant 3 PROPER factors (ie all the factors excluding the number itself), then 85 and 95 both have 3 proper factors.
No numbers between 1 and 100 have exactly eleven factors. 60, 72, 84, 90 and 96 each have twelve factors.
1 is the only number between 1 and 100 that has too few factors to be a prime number.
There aren't any numbers between 1 and 100 with 16 factors.
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1
There are five numbers in that range with 12 factors, but none with exactly eleven.