Compute the prime factors of a given natural number.
A prime number is only evenly divisible by itself and 1.
Note that 1 is not a prime number.
What are the prime factors of 60?
Our successful divisors in that computation represent the list of prime factors of 60: 2, 2, 3, and 5.
You can check this yourself:
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The Prime Factors Kata by Uncle Bob http://butunclebob.com/ArticleS.UncleBob.ThePrimeFactorsKata
(* prime-factors - 1.1.0 *) open Base open OUnit2 open Prime_factors (* Assert Equals *) let ae exp got _test_ctxt = let printer xs = List.map xs ~f:Int64.to_string |> String.concat ~sep:";" in assert_equal exp got ~printer let to_int64s = List.map ~f:Int64.of_int (* 64 bits integers are needed for the last number. * * If you happen to use a 64 bits machine normal ints would do as well, but this * works for everybody. *) let tests = [ "no factors" >:: ae (to_int64s ) (factors_of 1L); "prime number" >:: ae (to_int64s ) (factors_of 2L); "square of a prime" >:: ae (to_int64s [3; 3]) (factors_of 9L); "cube of a prime" >:: ae (to_int64s [2; 2; 2]) (factors_of 8L); "product of primes and non-primes" >:: ae (to_int64s [2; 2; 3]) (factors_of 12L); "product of primes" >:: ae (to_int64s [5; 17; 23; 461]) (factors_of 901255L); "factors include a large prime" >:: ae (to_int64s [11; 9539; 894119]) (factors_of 93819012551L); ] let () = run_test_tt_main ("prime-factors tests" >::: tests)
module L = Int64 let factors_of n = let rec factorise ?(fact=2L) ?(facts=) = function | 1L -> List.rev facts | i when L.rem i fact = 0L -> factorise ~fact:fact ~facts:(fact::facts) (L.div i fact) | i -> factorise ~fact:(L.add fact 1L) ~facts:facts i in factorise n
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