16
625
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.
240 is the smallest number with at least 19 factors. 240 has twenty factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 262144 is the smallest number with EXACTLY 19 factors
It must have at least 3 factors.
64
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
36
625
Oh, dude, the least number with exactly 8 factors is 24. It's like, got factors 1, 2, 3, 4, 6, 8, 12, and 24. So, yeah, that's the magic number with just the right amount of factors to make it cool.
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).
2 (1 and 2)
3*5*7*9 = 945 ...check if any number less than that has exactly four distinct factors.
The number 64 is the least number that has exactly 7 factors because it is a perfect power of a prime, specifically (2^6). The number of factors of a number can be determined using the formula ((e_1 + 1)(e_2 + 1)...(e_n + 1)), where (e_i) are the exponents in its prime factorization. For 64, the factorization is (2^6), leading to ((6 + 1) = 7) factors. Smaller numbers either have fewer factors or do not meet the requirement of having exactly 7.
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.
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.