The smallest number with exactly eight factors is 24.
64 is the least number having exactly 7 factors: 1, 2, 4, 8, 16, 32, and 64.
100.....1,2,4,5,10,20,25,50,100
625
None since 2014 is an even number so the date will be composite. Composite numbers have at least three factors.
If you disregard 1 and the number itself, then 12, with the factors 2, 3, 4 and 6. If you include 1 and the number itself, then 6 with factors 1, 2, 3 and 6.
16
64
3*5*7*9 = 945 ...check if any number less than that has exactly four distinct factors.
6
4096 is the smallest number with exactly 13 factors. (Including 1 and itself as factors).192 is the smallest number with exactly 13 properfactors, (excluding the number itself).120 is the smallest number with at least 13 factors (it has 16 factors)To find the smallest number with exactly N factors (for example, N=12):Factor N into primes, (for example, 12= 2*2*3Subtract 1 from each of the prime factors (for example, 1,1,2)Sort them by largest first (for example, 2,1,1)Raise successive prime numbers to these powers (for example, 2^2,3^1,5^1)Multiply these together (for example: 4*3*5 = 60; 60 is the smallest number with exactly 12 factors).
A prime number must have exactly two factors. 12543672 ends in a 2, therefore it can be halved. This means that the factors are at least 1, 2, and 12543672, so it is not a prime number.