6227020800
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Rishipoddar, are you sure? Can you list the 13 factors that you are using? Interpreting "exactly 13 factors" to mean that the factors are unique, the number has to be the product of 1 and the first 11 prime numbers starting with 2, unless I am making a serious error. The product of these 12 factors is then the 13th factor. I calculate 200560490130. The factors are 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and the number itself, the product of the previous 12 factors.
The number you offer uses 2 as a factor ten times (2 to the 10th power), 3 as a factor 5 times (3 to the 5th power), and 5 as a factor 2 times (5 squared). Then the numbers 7, 11 and 13 are each used once. If that is allowed, then the actual answer is 1 (one), simply the use of 1 as a factor 13 times. Or if 1 is not allowed, then the answer could be 2 to the power 13: 8192. It is possible that I do not understand the question.
I vote for 212 =4096 , factors are 1,2,4,8,16,32,64,128,256,512,1024,2048,and 4096.
If I'm reading the question correctly, X = 6 (not a prime number). 3X = 18, and its four factors are 1, 2, 3 and 9
If p, q and r are distinct primes and n=pxqxr then n will have 8 factors, all of which will be positive since prime numbers are all positive, which are: n(pqr), pq, pr, qr, p, q, r and 1. Here there were 3 distinct primes so the number of positive factors is 2^3. In general if you had p distinct primes then you would have 2^p positive factors.
32
There can be infinitely many distinct factors.
24edit: nonethe smallest number with 12 distinct factors would be2*3*5*7*11*13*17*19*23*29*31*37>>100
It is 4096.
3
4 and 9
A positive integer with exactly two distinct factors.
Prime squares have three factors. There are 11 of them in that range.
3*5*7*9 = 945 ...check if any number less than that has exactly four distinct factors.
156
The difference is one.
If I'm reading the question correctly, X = 6 (not a prime number). 3X = 18, and its four factors are 1, 2, 3 and 9
Prime numbers to the 12th power, like 4096 or 531441.
Any prime to the 12th power, like 4096 or 531441
If p, q and r are distinct primes and n=pxqxr then n will have 8 factors, all of which will be positive since prime numbers are all positive, which are: n(pqr), pq, pr, qr, p, q, r and 1. Here there were 3 distinct primes so the number of positive factors is 2^3. In general if you had p distinct primes then you would have 2^p positive factors.