Demo: Divisibility Rules of 5, 6 and 7

Duration: 12 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About the course: About the Course
  2. Mathematical Aptitude: संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Divisibility Rules, प्रतिशत / Percentage, अनुपात और समानुपात / Ratio and Proportion, औसत / Average, लाभ, हानि और बट्टा / Profit, Loss and Discount, समय और कार्य / Time and Work, घन क्षेत्रमिति / Solid Mensuration, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय, चाल और दूरी / Time, Speed and Distance, Age Problems, मिश्रण और एलिगेशन / Mixture and Alligation, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Pipe and Cistern, Trigonometry, Statistics, आँकड़ा निर्वचन / Data Interpretation, Arithmetic, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Logical Reasoning: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, सादृश्यता एवं वर्गीकरण / Analogy and Classification, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, क्रम एवं रैंकिंग / Order and Ranking, अशाब्दिक तर्क / Non-Verbal Reasoning, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, Syllogisms, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Analytical Reasoning (Counting Figures Reasoning), घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, कैलेंडर एवं घड़ी / Calendar and Clock, Clock
  4. General Knowledge: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Chemistry, Biology, History, Geography, Polity, Indian Economy, समसामयिकी / Current Affairs, Static General Knowledge, राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge
  5. Art of Teaching: शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन / Teaching-Learning Process and Classroom Management, Learners & Learning Process, Factors Affecting Teaching, शिक्षण विधियाँ एवं उपागम / Teaching Methods and Approaches, सूक्ष्म शिक्षण एवं कक्षा संप्रेषण / Microteaching and Classroom Communication, शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी / Teaching Aids and Educational Technology, आकलन एवं मूल्यांकन / Assessment and Evaluation, शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास / Teacher: Qualities, Professional Ethics and Development, शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन / Educational Policies, Acts and Administration, पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र / Curriculum, Arts and Co-curricular Areas, निर्देशन एवं परामर्श / Guidance and Counselling, दिव्यांग बच्चों की शिक्षा / Education of Children with Disabilities, Micro-Teaching & Teaching Skills, पाठ योजना / Lesson Planning
  6. Environmental Science: Environment
  7. Unit 1 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  8. Unit 2 | COA: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer
  9. Unit 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  10. Unit 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Unit 4 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  12. Unit 5 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  13. Unit 6 | 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, Transaction Management, Concurrency Control
  14. Unit 7 | Computer Networks: Introduction to CN, Data Communication, 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
  15. Unit 8 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  16. Unit 9 | Object Oriented Programming: OOPS with C++
  17. Unit 10 | Web Development: HTML Basics, CSS, JavaScript-Basics, XML, Node.js, Git & Github, PHP
  18. Unit 11 | 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
  19. Unit 12 | IoT: Emerging Tech Trends, Cloud Computing, कंप्यूटर नेटवर्क / Computer Networks
  20. Unit 13 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Unit 14 | E-Commerce: Electronic Data Interchange and E-Commerce, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Physical Security and Cryptography Basics, Cyber Safety and Security
  22. Unit 15 | Multimedia: Multimedia
  23. Unit 16 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  24. Full Length Mock Tests — General Paper:
  25. Full Length Mock Tests — Computer Science (Paper II):
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a structured lesson on divisibility rules for the numbers 5, 6, and 7. The instructor begins by establishing the fundamental rule for divisibility by 5: a number is divisible if its last digit is either 0 or 5. This concept is reinforced through immediate examples, such as identifying 175 as divisible and 809 as not. The lesson then transitions to composite numbers, introducing a method where the divisor is broken down into factors (P = a x b) to simplify testing. The instructor demonstrates this with the number 6, requiring numbers to be both even and divisible by 3. The final section focuses on the number 7, presenting a specific arithmetic trick involving doubling the last digit and subtracting it from the remaining number to determine divisibility. The video concludes with a summary of these rules and examples verifying their application.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lesson opens with the divisibility rule for 5, explicitly stating that a number is divisible if its last digit is 0 or 5. The instructor uses on-screen text to underline these key digits and provides immediate verification examples: 175 is marked 'Yes' because it ends in 5, while 809 is marked 'No'. The instructor then introduces the concept of composite numbers using fraction notation N/P and factorization P = a x b, setting up the framework for testing divisibility by products of factors.

  2. 2:00 – 5:00 02:00-05:00

    The instructor applies the composite number rule to demonstrate divisibility for products like 2x3=6 and 3x4=12. Specific examples are analyzed, such as breaking down the number 28 into factors 7 x 4. The focus shifts to the divisibility rule for 6, which requires a number to satisfy two conditions: it must be even and divisible by 3. The instructor verifies this with 114, showing the sum of digits (1+1+4=6) is divisible by 3, while 308 fails because the digit sum (11) is not divisible by 3.

  3. 5:00 – 10:00 05:00-10:00

    A specific trick for divisibility by 7 is introduced using the number 672. The method involves isolating the last digit (2), multiplying it by 5, and adding the result to the remaining number (67 + 10). The instructor then demonstrates a shortcut method where the last digit is doubled and subtracted from the rest. This process is applied to 672 (67 - 4 = 63, which is divisible by 7) and 105 (10 - 2 = 8, not divisible by 7), with visual annotations showing the arithmetic steps and final verification.

  4. 10:00 – 12:29 10:00-12:29

    The lesson concludes with a formal summary of the divisibility rule for 7, displayed as text: 'Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7.' The instructor tests this rule on 905, calculating 90 - (2*5) = 80, which is not divisible by 7. Examples of 672 and 105 are revisited to confirm their status as divisible or not. The video ends with a 'THANKS FOR WATCHING' screen, marking the completion of the instructional content.

The video systematically builds mathematical understanding by moving from simple single-digit rules to more complex composite and prime number strategies. The progression starts with the visual simplicity of checking the last digit for 5, then introduces logical conjunctions (AND conditions) for composite numbers like 6. The most complex concept, divisibility by 7, is taught through algorithmic tricks that transform the original number into a smaller, more manageable one. The instructor consistently uses visual cues like underlining, circling, and color-coded text to highlight critical steps in the calculation process. This pedagogical approach ensures that students can follow the logical flow from definition to application, reinforcing each rule with concrete numerical examples before moving to the next concept.

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