The question is how many positive divisors do each of the following numbers have:
1) 6
2) 48
3) 100
4)
5)
6) 0
I understand how to do #1, #2, and #3. For example:
positive divisors. (which happen to be 1, 2, 3, and 6)
I used the same method (converting each number to a factor of primes in exponential notation, adding 1 to each exponent, and multiplying the exponents) to solve #2 and #3.
I'm not sure where to start on 4, 5, or 6. Could anyone shed some light on the correct method for doing these problems?
Thanks, I think I see the pattern. That's beautiful.
For #4 there are n + 1 factors because:
(there are 4 positive divisors of 8)
(there are 5 positive divisors of 16)
For #5 there are factors because:
(there are 9 positive divisors of 100)
(there are 16 positive divisors of 1000)
I understand the pattern above. But what if the question was a number other than or ? Is there a way to find the number of positive divisors for, say, ?
For #6: Zero divided by any number (except zero, because that is undefined) should be zero. So the answer would be the set of all numbers not equal to zero?
Yes, that makes sense. There are (5)(3)(7)(2) positive divisors because has (4 + 1) divisors, has (2 + 1) divisors, has (6 + 1) divisors, and has (1 + 1) divisors.
So, does this only work with prime numbers? Is it not possible to do this with or or ?
Because does not have factors... For example:
positive divisors.