Problem 42615. Factorizing a number into a given number of factors

Given a positive integer, n, and another positive integer, b, return a matrix, M, of width b, with the following properties: (a) Each row is sorted in ascending order (b) the rows are unique (c) the product of the integers in each row equals n (d) the columns are sorted in ascending order, such that the primary sorting is based on the first column, secondary on the second column, etc. (e) M contains integer values only

Note: The number 1 is also considered a valid factor.

Example 1:

n = 30

b = 2

M = [ 1 30 ; 2 15 ; 3 10 ; 5 6 ]

Example 2:

n = 120

b = 3

M = [ 1 1 120 ; 1 2 60 ; 1 3 40 ; 1 4 30 ; 1 5 24 ; 1 6 20 ; 1 8 15 ; 1 10 12 ; 2 2 30 ; 2 3 20 ; 2 4 15 ; 2 5 12 ; 2 6 10 ; 3 4 10 ; 3 5 8 ; 4 5 6 ]