Divisibility Rules of 11, 12 and 13

Duration: 11 min

This video lesson is available to enrolled students.

Return to /learn/BPSC/part-2-primary-maths/divisibility-rules/divisibility-rules-for-all-numbers/asset-divisibility-rules-of-11-12-and-13 after enrolling

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, अनुक्रम, श्रेणी और संयोजन / Sequences, Series and Combinatorics, 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 overview of divisibility rules for numbers 2 through 13, presented by an instructor in a screen recording format. The lecture begins with a colorful, hand-drawn wheel diagram that visually organizes the rules for divisibility by 2, 3, 4, 5, 6, 9, and 10, using examples and key phrases like 'ends in' and 'sum of the digits'. The presentation then transitions to a more formal slide format, where the instructor explains the rule for divisibility by 11, which involves subtracting the last digit from the number formed by the remaining digits, and demonstrates this with examples like 286 and 14641. The video continues with the rule for divisibility by 12, which is based on the principle that a number is divisible by 12 if it is divisible by both 3 and 4, illustrated with the numbers 648 and 524. A key concept introduced is that if a number is divisible by a composite number, it is also divisible by all of its factors, with examples for 6 and 12. The final segment covers the rule for divisibility by 13, which requires adding four times the last digit to the remaining number, demonstrated with the example 5061. 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. It then transitions to a colorful, hand-drawn circular diagram titled 'DIVISIBILITY RULES'. This diagram is divided into sections for different numbers, each explaining a rule. For example, the rule for 2 is 'is an even number', for 5 it's 'ends in 0 or 5', and for 9 it's 'the sum of the digits is divisible by 9'. The instructor, Yash Jain Sir, is visible in a small window, explaining the concepts. The diagram also includes a section for 6, stating it is 'divisible by 2 AND 3'. The visual style is highly illustrative and engaging, using bright colors and arrows to connect concepts.

  2. 2:00 – 5:00 02:00-05:00

    The video shifts to a new slide titled 'Another Rule For 11'. The rule is stated as: 'Subtract the last digit from a number made by the other digits.' The instructor demonstrates this with the example 286: 28 - 6 = 22, and since 22 is divisible by 11, 286 is also divisible by 11. He then applies the rule to 14641: 1464 - 1 = 1463, then 146 - 3 = 143, then 14 - 3 = 11, and since 11 is divisible by 11, 14641 is also divisible by 11. The instructor uses red ink to write out the steps on the slide, emphasizing the process of repeated application.

  3. 5:00 – 10:00 05:00-10:00

    The next slide, titled '12', explains that a number is divisible by 12 if it passes both the divisibility rules for 3 and 4. The instructor demonstrates this with the number 648: the sum of its digits (6+4+8=18) is divisible by 3, and the last two digits (48) form a number divisible by 4, so 648 is divisible by 12. For 524, the sum of digits (5+2+4=11) is not divisible by 3, so 524 is not divisible by 12. The video then introduces a new concept: 'Factors Can Be Useful'. It explains that if a number is divisible by a composite number, it is also divisible by each of its factors. For example, if a number is divisible by 12, it is also divisible by 2, 3, 4, and 6. The instructor writes the factors of 12 as {1, 2, 3, 4, 6, 12}.

  4. 10:00 – 11:06 10:00-11:06

    The final topic is the divisibility rule for 13. The rule is to 'Add four times the last digit to the remaining leading truncated number.' The instructor demonstrates this with the number 5061: 506 + (1*4) = 510, then 51 + (0*4) = 51, then 5 + (1*4) = 9. Since 9 is not divisible by 13, 5061 is not divisible by 13. The instructor then corrects the example, showing that for 5061, the correct calculation is 506 + (1*4) = 510, then 51 + (0*4) = 51, then 5 + (1*4) = 9, which is not divisible by 13. The video ends with a 'THANKS FOR WATCHING' screen.

The video presents a structured and progressive lesson on divisibility rules, moving from a visually engaging overview to detailed, step-by-step demonstrations. It begins with a comprehensive diagram for basic rules (2, 3, 4, 5, 6, 9, 10), establishing a foundation. The core of the lesson focuses on more complex rules for 11 and 13, using a consistent method of explanation: stating the rule, providing a clear example, and showing the calculation process. A key pedagogical point is the introduction of the concept that divisibility by a composite number implies divisibility by its factors, which is a powerful shortcut for students. The instructor's use of a screen recording with on-screen annotations allows for a clear, focused presentation of the mathematical logic, making the content accessible for revision and learning.

Loading lesson…