Project Euler #3

03.lua

--[[
The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?
--]]

function get_all_factors(number)
    local factors = {}
    for possible_factor=1, math.sqrt(number), 1 do
        local remainder = number%possible_factor

        if remainder == 0 then
            local factor, factor_pair = possible_factor, number/possible_factor
            table.insert(factors, factor)

            if factor ~= factor_pair then
                table.insert(factors, factor_pair)
            end
        end
    end

    table.sort(factors)
    return factors
end

the_universe = 600851475143
factors_of_the_universe = get_all_factors(the_universe)

print("Count",  "The Factors of Life, the Universe, and Everything")
table.foreach(factors_of_the_universe, print)

--[[
Count   The Factors of Life, the Universe, and Everything
1   1
2   71
3   839
4   1471
5   6857
6   59569
7   104441
8   486847
9   1234169
10  5753023
11  10086647
12  87625999
13  408464633
14  716151937
15  8462696833
16  600851475143
--]]