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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.
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If X is positive is X prime A X3 has exactly four distinct positive integer factors B X2-X-6 0?
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 told that 'q' 'p' and 'r' are distinct primes and that there exists 'n' such that 'n equals p x q x r' How many positive factors of 'n' are there and How do you determine what they are?
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.
How many positive integers less than 100 have exactly 4 factors?
32
How many distinct factors?
There can be infinitely many distinct factors.
Which numbers less than 100 have exactly 12 distinct factors?
24edit: nonethe smallest number with 12 distinct factors would be2*3*5*7*11*13*17*19*23*29*31*37>>100
