Divisibility Rules of 17 and 18

Duration: 12 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, शब्द-भंडार, अपठित बोध, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): رسم الخط، حروفِ تہجی اور املا / Script, Alphabet and Spelling, اسم، ضمیر اور صفت / Nouns, Pronouns and Adjectives, الفاظ، محاورے اور ضرب الامثال / Vocabulary, Idioms and Proverbs, تفہیمِ عبارت، انشا اور ترجمہ / Comprehension, Writing and Translation, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): শব্দার্থ, বাগধারা ও ভাষাশুদ্ধি / Meaning, Idioms and Correct Usage, বাক্য ও বাচ্য / Sentences and Voice, শব্দগঠন ও শব্দভান্ডার / Word Formation and Vocabulary, অনুবাদ, বোধপরীক্ষণ ও রচনা / Translation, Comprehension and Composition
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Pronoun, Verb, Adverb, Prepositions and Conjunctions, Parts of Speech, Determiner, Conjunction, Modals, Transformation of Sentences, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Structure and Common Errors, Reading Comprehension, Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, अशाब्दिक तर्क / Non-Verbal Reasoning, प्रतिशत / Percentage, औसत / Average, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय और कार्य / Time and Work, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Algebra, Probability, Trigonometry, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, Data Arrangement, Inequality, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, 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
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, Chemistry, History, Geography, Indian Economy, Environment, समसामयिकी / Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, कंप्यूटर नेटवर्क / Computer Networks, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), Terms & Abbreviations, प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References, OOPS with Java
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
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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