# Problem 36

Construct a list containing the prime factors and their multiplicity for a given integer.

## Example

``````primeFactorsM 315 = [(3, 2), (5,1), (7,1)]
``````

## Unit Test

``````import Html
import List

primeFactorsM : Int -> List ( Int, Int )
primeFactorsM n =
[]

main =
Html.text
(if (test) then
else
"Your implementation failed at least one test."
)

test : Bool
test =
List.all (\( result, expect ) -> result == expect)
[ ( primeFactorsM 36, [ ( 2, 2 ), ( 3, 2 ) ] )
, ( primeFactorsM 10, [ ( 2, 1 ), ( 5, 1 ) ] )
, ( primeFactorsM -1, [] )
, ( primeFactorsM 1, [] )
, ( primeFactorsM 0, [] )
, ( primeFactorsM 120, [ ( 2, 3 ), ( 3, 1 ), ( 5, 1 ) ] )
, ( primeFactorsM 2, [ ( 2, 1 ) ] )
, ( primeFactorsM 23, [ ( 23, 1 ) ] )
, ( primeFactorsM 69146, [ ( 2, 1 ), ( 7, 1 ), ( 11, 1 ), ( 449, 1 ) ] )
, ( primeFactorsM 9007, [ ( 9007, 1 ) ] )
, ( primeFactorsM 36028, [ ( 2, 2 ), ( 9007, 1 ) ] )
, ( primeFactorsM 26028, [ ( 2, 2 ), ( 3, 3 ), ( 241, 1 ) ] )
]
``````

## Hints

1. Combine code from problems 9, 10 and 35

Solutions