Divisibility by 8 Explained | Last 3 Digits Rule Proof Java Code | Big Numbers Trick

“Why Only Last 3 Digits Matter? | Divisibility by 8 Full Proof + Code” “Divisible by 8 Trick | Modular Arithmetic Explained (With C++ & Java)” “Check Divisibility by 8 for Large Numbers | Last 3 Digits Logic!” In this video, we break down one of the most interesting number system shortcuts: **A number is divisible by 8 if and only if its last 3 digits are divisible by 8.** We start from first principles using modular arithmetic: N = 1000k + abc → 1000k mod 8 = 0 → N mod 8 depends only on the last three digits. You will learn: ✔ Why 1000 ≡ 0 (mod 8) ✔ Full proof of the “last three digits rule” ✔ Big number divisibility using strings ✔ Brute Force approach using BigInteger / C++ long long ✔ Efficient solution using only last 3 digits ✔ Time complexity breakdown ✔ Bit manipulation intuition (optional) #DivisibilityRules #ModularArithmetic #JavaProgramming #CPPProgramming #MathTricks #NumberTheory #CodingInterviewPrep #BigInteger #BitManipulation #dsa Whether you're preparing for FAANG, product-based companies, coding rounds, or want to strengthen your fundamentals, this channel brings you the best structured DSA explanations with zero confusion. Step-by-step logic Mathematical reasoning Multiple approaches (Naive → Optimized) Time & Space complexity Real interview insights Clean and easy-to-understand code Data Structures (Arrays, Strings, Stacks, Queues, Trees, Graphs, LinkedList, Hashing, Heaps) Algorithms (Sorting, Searching, Binary Search, Greedy, DP, Recursion, Backtracking, Graph Algorithms) Math Logic for coding (Number Theory, Combinatorics, Modular Arithmetic) Coding interview questions with full proof and code Competitive programming tricks and optimizations LeetCode, GFG, Codeforces, HackerRank problem explanations Pattern printing & logic building Time complexity mastery 👍 Like the video 💬 Comment your doubts 🔔 Subscribe for daily coding content 📤 Share with your coding friends Your support motivates me to create more high-quality content. Tags: #DSA #Coding #CompetitiveProgramming #Programmer #DataStructures #Algorithms #LeetCode #GeeksForGeeks #CodingInterview #SoftwareEngineer #CodeWithMe #MathInCode #Optimization #CP #Java #Python #C++ #LogicBuilding #ProblemSolving #TechInterview #ProgrammingTutorial #ComputerScience #CodingChallenge #DSATutorial #CodingForBeginners #Code #BinarySearch #Recursion #DynamicProgramming coding, dsa, data structures and algorithms, competitive programming, problem solving, coding interview, interview preparation, geeks for geeks, leetcode solutions, codeforces, hackerRank, programming tutorial, algorithm explanation, data structures tutorial, dynamic programming, recursion, binary search, greedy algorithms, coding tricks, optimize code, coding shortcuts, math logic in code, beginners coding, java coding, python coding, cpp coding, technical interview, placements preparation, coding questions, solved problems, coding solution, youtube coding channel, logic building, number theory, mathematics for coding, time complexity, space complexity