From 54b8f3c5f0cb4cba0dd21134e48e4d0af542102b Mon Sep 17 00:00:00 2001
From: Matthew Ellison <matthew@localhost.localdomain>
Date: Thu, 7 Feb 2019 11:43:34 -0500
Subject: [PATCH] Added a function to get all divisors of a number

---
 Algorithms.lua | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)

diff --git a/Algorithms.lua b/Algorithms.lua
index b93c27f..87c0aae 100644
--- a/Algorithms.lua
+++ b/Algorithms.lua
@@ -136,3 +136,35 @@ function getFactors(goalNumber)
 	--Return the list of factors
 	return factors;
 end
+
+function getDivisors(goalNumber)
+	local divisors = {};
+	--Start by checking that the number is positive
+	if(goalNumber <= 0) then
+		return divisors;
+	--If the number is 1 return just itself
+	elseif(goalNumber == 1) then
+		divisors[#divisors+1] = 1;
+	--Otherwise add 1 and itself to the list
+	else
+		divisors[#divisors+1] = 1;
+		divisors[#divisors+1] = goalNumber;
+	end
+
+	--Start at 3 and loop through all numbers < (goalNumber / 2) looking for a number that divides it evenly
+	local topPossibleDivisor = math.ceil(math.sqrt(goalNumber));
+	for possibleDivisor=2,topPossibleDivisor do
+		--If you find one add it and the number it creates to the list
+		if((goalNumber % possibleDivisor) == 0) then
+			divisors[#divisors+1] = possibleDivisor;
+			--Account for the possibility of sqrt(goalNumber) being a divisor
+			if(possibleDivisor ~= topPossibleDivisor) then
+				divisors[#divisors + 1] =(goalNumber / possibleDivisor);
+			end
+		end
+	end
+	--Sort the list before returning for neatness
+	table.sort(divisors);
+	--Return the list
+	return divisors;
+end