# Problem 36

(Intermediate ðŸŒŸðŸŒŸ) Determine the prime factors and their multiplicities of a given positive integer.

Construct a list containing each prime factor and its multiplicity.

```
partial def primeFactorsMult (n : Nat) : List (Nat Ã— Nat) :=
sorry
-- The following codes are for test and you should not edit these.
#guard primeFactorsMult 0 = []
#guard primeFactorsMult 1 = []
#guard primeFactorsMult 2 = [(2, 1)]
#guard primeFactorsMult 315 = [(3, 2), (5, 1), (7, 1)]
#guard primeFactorsMult 307 = [(307, 1)]
#guard primeFactorsMult 1000 = [(2, 3), (5, 3)]
#guard primeFactorsMult 990801529 = [(31477, 2)]
#guard primeFactorsMult 119883030485877764933
= [(104623, 1), (104639, 2), (104651, 1)]
```