Short Tricks to Find Unit Digit of an Expression (1)

Duration: 15 min

This video lesson is available to enrolled students.

Return to /learn/ZERO-TO-HERO/aptitude/number-system-bff2d7/unit-digit-last-digit-concepts/asset-short-tricks-to-find-unit-digit-of-an-expression-1 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  2. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Virtual Memory, Disc Scheduling, File Management, Memory Management, Threads & Process Creation
  6. Computer Networks: Introduction to CN, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Network Security, Hardware Basics
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  11. C language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums
  12. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Emerging Trends & AI: Emerging Tech Trends, Artificial Intelligence, Cloud Computing
  14. Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing
  15. Aptitude: Percentage, Ratio and Proportion (Ratios), Logarithm, HCF LCM, Divisibility Rules, Average, Sequence and Series (Series), Number System, Powers and Exponents (Surds and Indices), Algebra, Permutation and Combination, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Data Interpretation, Arithmetic, Speed Mathematics and Basic Mathematics, TCS NQT Advanced Quantitative Ability, Gamified / Game Based Aptitude, Linear Algebra, Trigonometry
  16. Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  17. English (Verbal Ability): Vocabulary, Noun, Pronoun, Adjectives, Preposition, Articles, Direct and Indirect Speech, Tenses, Conjunction, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Interjection, Verb, English Writing Ability
  18. Engineering Mathematics: Calculus, Vectors
  19. GATE Live Class Recordings 2026: GATE 2026 Live Class
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a comprehensive lecture on the concept of 'Unit Digit' in number systems, presented by an instructor from Knowledge Gate Eduventures. The video begins with an introduction to the topic, emphasizing its importance for various competitive exams such as CAT, XAT, GMAT, and government tests, where it is a crucial part of the aptitude section. The core of the lecture focuses on a method to find the unit digit of large numbers raised to high powers. The instructor explains that this is achieved by identifying the cyclicity of the unit digit of the base number. The method involves observing the pattern of unit digits as the base is raised to successive powers. The video provides a classification of single-digit numbers (0-9) into three categories based on their cyclicity: numbers with a fixed unit digit (0, 1, 5, 6), numbers with a two-number cycle (4, 9), and numbers with a four-number cycle (2, 3, 7, 8). The instructor demonstrates this concept with several examples, including 185^563, 271^6987, and 156^25369, showing how to determine the unit digit by finding the remainder when the exponent is divided by the cycle length. The video concludes with a summary of the method and a list of practice problems for the viewer.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for 'NUMBER SYSTEM' and a subtitle 'The mysterious world of numbers...'. The instructor, Yash Jain, introduces the topic, stating that it is a fundamental concept for various competitive exams. A slide titled 'Why Study This Topic?' lists numerous exams including CAT, XAT, CMAT, NMAT, SNAP, MAT, IIFT, GMAT, GATE, and others, emphasizing that number system is a crucial part of the aptitude section, with at least two questions appearing in every exam. The instructor is visible in a small window in the bottom right corner, speaking to the camera.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to explain the importance of the topic, with a list of exams on the screen. He emphasizes that the number system is a key area for aptitude tests. The slide lists exams such as Placements, Government Exams, Civil Services Exams, Banking Exams, Railway Exams, College Entrance Exams, and others. The instructor's voiceover explains that this topic is essential for students preparing for these competitive exams. The visual focus remains on the list of exams, with the instructor's video feed in the corner.

  3. 5:00 – 10:00 05:00-10:00

    The video transitions to a new slide titled 'Concept of Unit Digit'. The instructor explains that to find the unit digit of a number raised to a power, one must understand the concept of cyclicity. He states that the unit digit of a number repeats in a pattern when the number is raised to successive powers. The slide shows an example: 'Unit Digit of 3547^153 x 251^72'. The instructor then moves to a new slide with a question: 'Q: Find the unit digit of the following:', followed by a list of 11 problems, including 185^563, 271^6987, and 154^258741369. The instructor begins to solve the first problem, 185^563, by focusing on the unit digit of the base, which is 5.

  4. 10:00 – 14:35 10:00-14:35

    The instructor explains the rule for numbers ending in 0, 1, 5, or 6: their unit digit remains the same regardless of the power. He demonstrates this with 185^563, stating the unit digit is 5. He then moves to 271^6987, noting the unit digit of the base is 1, so the answer is 1. For 156^25369, the unit digit is 6. The instructor then explains the cyclicity of 4 and 9, which have a cycle of 2. He demonstrates with 154^258741369, where the unit digit of the base is 4, and the exponent is odd, so the unit digit is 4. He then explains the cycle of 2, 3, 7, and 8, which have a cycle of 4. He demonstrates with 190^654789321, where the unit digit of the base is 0, so the answer is 0. The video ends with a 'Thank You for Watching' screen.

The video provides a structured and practical guide to solving unit digit problems, a common type of question in competitive exams. It begins by establishing the relevance of the topic, then systematically introduces the core concept of cyclicity. The instructor uses a clear, step-by-step approach, first explaining the rules for numbers with fixed unit digits (0, 1, 5, 6), then for those with a two-number cycle (4, 9), and finally for those with a four-number cycle (2, 3, 7, 8). The method is demonstrated through a series of worked examples, showing how to determine the cycle length and use the remainder of the exponent divided by the cycle length to find the correct unit digit. This logical progression from theory to application makes the concept accessible and provides a reliable method for students to solve similar problems under time pressure.

Loading lesson…