Demo: Short Tricks to Find Number & Product of Factors

Duration: 11 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, Internet of Things
  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 introduction to the Number System, specifically focusing on Multiples and Factors. The lesson begins by defining multiples as an infinite set of numbers generated by multiplying a base number, exemplified by the sequence 3 = {3, 6, 9, ... ∞}. The instructor contrasts this with factors, which are finite divisors of a number. Using the integer 12 as a primary case study, the lecture demonstrates how to list factors manually and visually decompose numbers using factor trees. A critical distinction is drawn between general factorization (pairs like 1x12, 2x6) and prime factorization (breaking numbers into prime components like 2^2 x 3). The core of the lesson involves deriving and applying a formula to calculate the total number of factors based on prime exponents. Finally, the video concludes with a summary of these formulas and recommends memorizing specific ranges for squares, cubes, and multiplication tables to facilitate faster problem-solving.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for the 'Number System' chapter, establishing a progression from basic to advanced concepts. The instructor transitions immediately to the specific topic of 'Multiples and Factors.' On-screen text displays 'The mysterious world of numbers...' followed by the chapter title. The lesson formally introduces the concept of multiples, defining them as an infinite sequence. Evidence includes the visible text 'NUMBER SYSTEM' and 'MULTIPLES AND FACTORS,' alongside the instructor writing the set notation for multiples of 3 as '3 = { 3, 6, 9, 12, 15, 18, 21 ... ∞ }' to emphasize the infinite nature of this set.

  2. 2:00 – 5:00 02:00-05:00

    The instructor shifts focus to factors, contrasting their finite nature with the infinite set of multiples. Using the number 12 as a demonstration, the instructor lists factors sequentially: '{ 1, 2, 3, 4, 6, ... }'. The lesson visualizes factors as pairs through a factor tree method and division checks. Visible evidence includes the instructor writing '12/1', '12/2', '12/3 = 4', and '12/6 = 2' to validate divisors. The screen displays the complete set of factors for 12 as 'N = 12 = {1, 2, 3, 4, 6, 12}', explicitly labeling the set as 'Limited' compared to multiples.

  3. 5:00 – 10:00 05:00-10:00

    This segment distinguishes between general factorization and prime factorization. The instructor displays pairs like '1 x 12', '2 x 6', and '3 x 4' as general factorization. He then demonstrates prime factorization using a division method, resulting in the formula '12 = 2x2x3 = 2^2 x 3'. The core instructional goal is to teach the formula for counting factors: 'N = a^p x b^q x c^r' leading to the calculation '(p+1)(q+1)(r+1)...'. Applying this to 12, the instructor calculates '(2+1)(1+1) = 3x2=6' to confirm the manual count. The screen also shows '12 x 12 x 12 => (12)^3' in the context of product of factors.

  4. 10:00 – 11:06 10:00-11:06

    The video concludes by summarizing the key formulas for finding the number of factors and introduces a strategy for calculating products. The instructor revisits the factor count logic, showing 'no. of factors = 6/2 = 3' in the context of pairs. The final slide lists recommended memorization ranges for quick calculation: '1-100: Squares', '1-30: cube', and '1-50: tables'. The session ends with a 'THANK YOU FOR WATCHING' slide, reinforcing the educational content covered regarding number properties and factorization techniques.

The lecture systematically builds understanding of number properties, starting with the fundamental definition of multiples as infinite sets and factors as finite divisors. The instructor uses the number 12 to bridge these concepts, first listing factors manually and then introducing prime factorization as a more efficient method for analysis. A pivotal moment in the lesson is the derivation of the formula (p+1)(q+1)... which allows students to calculate the total number of factors without listing them all. This theoretical framework is supported by visual aids like factor trees and division checks. The lesson concludes with practical advice on memorizing squares, cubes, and tables to enhance computational speed, linking theoretical factorization skills to practical exam preparation strategies.

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