Divisibility Rules of 16

Duration: 15 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Section A: General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, History, Geography, Indian Economy, GK- Current Affairs, Evolution of Indian Banking (Banking & Financial Awareness), Environment
  3. Section A: General Intelligence & Reasoning ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Directions (Direction Test), 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
  4. Section A: Arithmetical & Numerical Ability: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Powers and Exponents (Surds and Indices), Algebra, Probability, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics, Miscellaneous
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Articles, Sentence Construction, Preposition, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Modals, Active Passive Voice (Voice), Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: Hindi Language & Comprehension: भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, 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, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  7. Section B: Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access 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, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics: Linear Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lesson on the divisibility rule for 16, presented by an instructor from Knowledge Gate Eduventures. The video begins with a title slide and a colorful, hand-drawn diagram illustrating various divisibility rules. The main content focuses on the rule for 16, which is explained through three distinct methods. The first method states that a number is divisible by 16 if its last four digits form a number divisible by 16, demonstrated with the example 157,648. The second method, for numbers with a thousands digit that is even, requires the last three digits to be divisible by 16, as shown with 254,176. The third method, for numbers with an odd thousands digit, requires the last three digits plus 8 to be divisible by 16, illustrated with 3408. The video also introduces a fourth method: adding the last two digits to four times the rest of the number, with examples like 176 and 1168. The instructor uses a digital whiteboard to write equations and perform calculations, and the video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide displaying 'DIVISIBILITY RULES' over a background of scattered numbers. This transitions to a colorful, hand-drawn diagram on a whiteboard, which is a circular chart with the title 'DIVISIBILITY RULES' at the center. The chart is divided into sections for different numbers (2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15), each with its corresponding rule written in a unique color. The instructor, Yash Jain Sir, is visible in a small window in the bottom right corner. The video then cuts to a new slide titled 'Divisibility Rule of 16', which states that 'The last four digits must be divisible by 16.' Three examples are provided: 157,648 is divisible by 16 (7,648 = 478 x 16), 157,648 is divisible by 16 (7,648 = 478 x 16), and 157,646 is not divisible by 16. The instructor's name and the channel 'KNOWLEDGE GATE EDUCATOR' are displayed at the bottom.

  2. 2:00 – 5:00 02:00-05:00

    The video displays a digital whiteboard with a list of powers of 2 written in red: 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32, 2^6 = 64. The instructor explains that since 16 is 2^4, the divisibility rule for 16 is based on the last four digits. He then draws a diagram with a circle labeled '1' and an arrow pointing to a box, which he uses to illustrate the concept of breaking down a number. He explains that for a number to be divisible by 16, the last four digits must be divisible by 16. The instructor then begins to demonstrate this rule by writing the number 157,648 on the board and focusing on the last four digits, 7,648. He performs a long division of 7,648 by 16, showing the steps: 16 into 76 is 4 (4 x 16 = 64), subtracting 64 from 76 gives 12, bringing down the 4 makes 124, 16 into 124 is 7 (7 x 16 = 112), subtracting 112 from 124 gives 12, bringing down the 8 makes 128, and 16 into 128 is 8 (8 x 16 = 128), resulting in a remainder of 0. This confirms that 7,648 is divisible by 16, and therefore 157,648 is divisible by 16.

  3. 5:00 – 10:00 05:00-10:00

    The video continues to explain the divisibility rule for 16. The instructor introduces a second method for numbers where the thousands digit is even. He writes the rule: 'If the thousands digit is even, the number formed by the last three digits must be divisible by 16.' He provides the example 254,176, where the thousands digit (4) is even. He then checks if 176 is divisible by 16. He performs the division: 16 into 176 is 11 (11 x 16 = 176), with a remainder of 0. He confirms that 176 is divisible by 16, so 254,176 is divisible by 16. He then introduces a third method for numbers where the thousands digit is odd. The rule is: 'If the thousands digit is odd, the number formed by the last three digits plus 8 must be divisible by 16.' He uses the example 3408, where the thousands digit (3) is odd. He calculates 408 + 8 = 416. He then checks if 416 is divisible by 16. He performs the division: 16 into 416 is 26 (26 x 16 = 416), with a remainder of 0. He confirms that 416 is divisible by 16, so 3408 is divisible by 16.

  4. 10:00 – 15:00 10:00-15:00

    The video presents a fourth method for checking divisibility by 16. The rule is: 'Add the last two digits to four times the rest. The result must be divisible by 16.' The instructor provides two examples. For 176, he calculates 1 (the rest) x 4 = 4, then adds the last two digits (76), resulting in 4 + 76 = 80. He checks if 80 is divisible by 16, which it is (80 = 5 x 16). For 1168, he calculates 11 (the rest) x 4 = 44, then adds the last two digits (68), resulting in 44 + 68 = 112. He checks if 112 is divisible by 16, which it is (112 = 7 x 16). The instructor then summarizes the three main rules for divisibility by 16, emphasizing the conditions based on the thousands digit. He also shows a diagram illustrating the process of dividing a number by 16, breaking it down into its components. The video concludes with a 'Thanks for Watching' screen.

  5. 15:00 – 15:21 15:00-15:21

    The video ends with a simple, dark purple screen with the text 'THANKS FOR WATCHING' in white, centered on the screen. This is a standard closing slide for the educational content.

The video systematically teaches the divisibility rule for 16 through a clear, step-by-step approach. It begins by establishing the foundational concept that 16 is 2^4, which leads to the primary rule: a number is divisible by 16 if its last four digits form a number divisible by 16. The instructor then presents two more specialized rules based on the parity of the thousands digit, providing a more efficient method for larger numbers. The lesson is reinforced with multiple worked examples for each rule, demonstrating the application of the concepts. The use of a digital whiteboard allows for clear, real-time explanations of the mathematical steps, making the content accessible for students preparing for competitive exams.

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