Divisiblity of 5 without using % and / operator

Question

how to check whether a number is divisible by 5 or not without using % and / operator. I want a quickest algorithm for this problem.

Answer 1

Let's represent the number in base 2. We have:

abcdefgh*101 = ABCDEFGHIJ

or

+abcdefgh00
+  abcdefgh
 ----------
 ABCDEFGHIJ

We are given ABCDEFGHIJ and want to find abcdefgh.

If you alternately - and + ABCDEFGH with its successive rightshift-by-2, you will get...

+  ABCDEFGH
-    ABCDEF
+      ABCD
-        AB
-----------
+  abcdefgh
+    abcdef
-    abcdef
-      abcd
+      abcd
+        ab
-        ab
-----------
   abcdefgh

The answer!