Since 7 is a prime, 7*1 = 7, so that the only possibility for a number to have 7 factors is to have only one prime factor to the power of 6, because 7 = 1 + 6.
64 = 26 = 7 factors (6 + 1) (2 is the smallest Prime number)
Since 36 > 100, then 64 is the only number between 0 and 100 that have 7 factors.
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There are a total of 14 numbers between 0 & 100 that are divisible by 7.
100 ÷ 4 = 25 → 24 numbers between 0 and 100 exclusive are divisible by 4 100 ÷ 6 = 16 2/3 → 16 numbers between 0 and 100 are divisible by 6 lcm(4, 6) = 12 → 100 ÷ 12 = 8 1/3 → 8 numbers between 0 and 100 are divisible by 4 and 6.
100
There are 19 numbers between zero and 365 that have an odd number of factors.
There are 8 square numbers between 0 and 100. 4, 9, 16, 25, 36, 49, 64, 81