diff --git a/Problem_Solving/Algorithms/2_Implementation/5_Between_Two_Sets.py b/Problem_Solving/Algorithms/2_Implementation/5_Between_Two_Sets.py
new file mode 100644
index 0000000..beff2e0
--- /dev/null
+++ b/Problem_Solving/Algorithms/2_Implementation/5_Between_Two_Sets.py
@@ -0,0 +1,63 @@
+
+#* There will be two arrays of integers. Determine all integers that satisfy the following two conditions:
+#*  1. The elements of the first array are all factors of the integer being considered
+#*  2. The integer being considered is a factor of all elements of the second array
+
+#* These numbers are referred to as being between the two arrays. Determine how many such numbers exist.
+
+a1 = [2, 3, 6]
+b1 = [42, 84]
+
+
+def getTotalX(a, b):
+
+    initial_numbers = list(range(max(a), min(b)+1))
+    for i in range(len(initial_numbers)):
+        for j in range(len(a)):
+            if initial_numbers[i] % a[j] != 0:
+                initial_numbers[i] = 0
+                continue
+
+    if 0 in initial_numbers:
+        initial_numbers = list(set(initial_numbers))[1:]
+    else:
+        initial_numbers = list(set(initial_numbers))
+
+    print('first loop results:',initial_numbers) #? for troubleshooting
+
+
+    for i in range(len(initial_numbers)):
+        for j in range(len(b)):
+            if b[j] % initial_numbers[i] != 0:
+                initial_numbers[i] = 0
+                break
+
+    if 0 in initial_numbers:
+        initial_numbers = list(set(initial_numbers))[1:]
+    else:
+        initial_numbers = list(set(initial_numbers))
+
+    print('second loop results:',initial_numbers) #? for troubleshooting
+    
+    return len(initial_numbers)
+
+
+# print(getTotalX(a1,b1))
+# first loop results: [36, 6, 42, 12, 18, 24, 30]
+# second loop results: [42, 6]
+# 2
+
+#? More elegant, compact solution below
+
+def getTotalX_two(a, b):
+    # Write your code here
+    factors = []
+    for i in range(a[-1], b[0]+1):
+        #? if ((number % element == 0) for all element in a) and
+        #?    ((element % number == 0) for all element in b)
+        if all(i % x == 0 for x in a) and all( x % i == 0 for x in b):
+            factors.append(i)
+    print(factors) #? for troubleshooting
+    return len(factors)
+
+print(getTotalX_two(a1,b1))
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diff --git a/Problem_Solving/Algorithms/2_Implementation/tempCodeRunnerFile.py b/Problem_Solving/Algorithms/2_Implementation/tempCodeRunnerFile.py
deleted file mode 100644
index 936189f..0000000
--- a/Problem_Solving/Algorithms/2_Implementation/tempCodeRunnerFile.py
+++ /dev/null
@@ -1,2 +0,0 @@
-print(subtractArray(a,b))
-# 21
\ No newline at end of file