Divisibility Rules of 17 and 18

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
  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 comprehensive lesson on divisibility rules, focusing on the number 17 and concluding with the rule for 18. The video begins with a title card and a colorful, circular diagram summarizing various divisibility rules. The main content is delivered by an instructor, Yash Jain, who explains three distinct methods for testing divisibility by 17. The first method involves subtracting five times the last digit from the remaining number, with an example demonstrating the process for 3978. The second method, introduced later, is to subtract the last two digits from two times the rest of the number, illustrated with the example 4675. The third method is to add nine times the last digit to five times the rest of the number, with examples including 4675 and 238. The video concludes with the divisibility rule for 18, which states a number is divisible by 18 if it is divisible by both 2 and 9, demonstrated with the number 342. The presentation uses a digital whiteboard for calculations and includes a copyright notice from Knowledge Gate Eduventures.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying 'DIVISIBILITY RULES' over a background of scattered numbers. This transitions to a colorful, circular diagram titled 'DIVISIBILITY RULES' which visually summarizes rules for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and 11. The instructor, Yash Jain, appears in a small window, introducing the topic. The main content begins with a slide titled 'Test for divisibility by 17,' which states the rule: 'Subtract five times the last digit from the remaining leading truncated number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.' An example is provided: '3978 --> 397 - 5*8 = 357 --> 35 - 5*7 = 0. So 3978 is divisible by 17.' The instructor begins to explain this rule, and the number 3978 is written on the board.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the divisibility test for 17 on the number 3978. He first identifies the last digit as 8 and calculates 5 times 8, which is 40. He then subtracts 40 from the remaining number, 397, to get 357. The process is repeated: the last digit of 357 is 7, and 5 times 7 is 35. Subtracting 35 from 35 gives 0. Since 0 is divisible by 17, the original number 3978 is also divisible by 17. The instructor uses a digital whiteboard to write out each step of the calculation, including the subtraction of 40 from 397 and the subsequent steps, clearly showing the process of reducing the number until a final result is reached.

  3. 5:00 – 10:00 05:00-10:00

    The video introduces a second divisibility rule for 17. The slide is titled 'Divisibility Rule of 17' and states: 'Subtract the last two digits from two times the rest.' An example is given: '4,675: 46 x 2 - 75 = 17.' The instructor demonstrates this with the number 4675. He takes the first part, 46, multiplies it by 2 to get 92, then subtracts the last two digits, 75, to get 17. Since 17 is divisible by 17, the original number is divisible by 17. The instructor then introduces a third rule: 'Add 9 times the last digit to 5 times the rest. Drop trailing zeroes.' Examples are provided: '4,675: 467 x 5 + 5 x 9 = 2380' and '238: 23 x 5 + 8 x 9 = 187.' He begins to work through the first example, calculating 467 x 5 and 5 x 9, and then adding the results.

  4. 10:00 – 12:14 10:00-12:14

    The instructor continues to demonstrate the third divisibility rule for 17. He completes the calculation for 4675, showing that 467 x 5 = 2335 and 5 x 9 = 45, which sum to 2380. He then applies the rule to 238, calculating 23 x 5 = 115 and 8 x 9 = 72, which sum to 187. The video then transitions to the divisibility rule for 18. The slide states: 'It is divisible by 2 and by 9.' An example is given: '342: it is divisible by 2 and by 9.' The instructor demonstrates this by checking if 342 is even (divisible by 2) and then summing its digits: 3 + 4 + 2 = 9, which is divisible by 9. The video concludes with a 'THANKS FOR WATCHING' screen.

The video systematically teaches three different methods for determining if a number is divisible by 17, each offering a unique approach to simplify the problem. The first method uses subtraction, the second uses a combination of multiplication and subtraction, and the third uses addition. This progression demonstrates that complex divisibility rules can be broken down into manageable steps. The lesson concludes with a standard rule for 18, reinforcing the concept that a number can be divisible by a composite number if it is divisible by its prime factors. The clear, step-by-step demonstrations on a digital whiteboard make the abstract rules concrete and easy to follow.

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