- #1

- 143

- 0

e.g. 24 has 4 factorizations

24 = 1 * 24

= 2 * 12

= 3 * 8

= 4 * 6

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- Thread starter PhDorBust
- Start date

- #1

- 143

- 0

e.g. 24 has 4 factorizations

24 = 1 * 24

= 2 * 12

= 3 * 8

= 4 * 6

- #2

Mark44

Mentor

- 34,826

- 6,570

For a given number n, determine whether the numbers in the set {2, 3, 4, ..., m} are divisors, where m <= √n. You don't need to check for 1 being a divisor.

e.g. 24 has 4 factorizations

24 = 1 * 24

= 2 * 12

= 3 * 8

= 4 * 6

You can tweak the process some: if n is odd, then it won't be divisible by any even number.

- #3

- 143

- 0

These are my thoughts. To find the number of factorizations of a number, find its prime factorization, then I *believe* there is some expression for the number of factors given this prime factorization.

For example, given a number p^n, it will have n + 1 unique factorizations. I've written out the cases for (p1^n) * (p2 ^ m), where p,p1,p2 are arbitrary primes; but I am not getting the pattern for arbitrary (p1 ^ r1) ... (pn ^ rn) factorizations.

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