Demo: Tricky Important Questions on Finding Product of Factors

Duration: 10 min

This video lesson is available to enrolled students.

Return to /learn/BIHAR-STET-COMPUTER-SCIENCE-COMPLETE-COURSE/mathematical-aptitude/number-system-bff2d7/factors-multiples-prime-factorization/asset-demo-tricky-important-questions-on-finding-product-of-factors after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the course: About the Course
  2. Mathematical Aptitude / गणितीय अभिक्षमता: Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Divisibility Rules / विभाज्यता के नियम, Percentage / प्रतिशत, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time, Speed and Distance / समय, चाल और दूरी, Age Problems / आयु संबंधी प्रश्न, Mixture and Alligation / मिश्रण और एलिगेशन, Algebra / बीजगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Pipe and Cistern / नल और टंकी, Trigonometry / त्रिकोणमिति, Statistics / सांख्यिकी, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  3. Logical Reasoning / तार्किक तर्कशक्ति: Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Order and Ranking / क्रम एवं रैंकिंग, Non-Verbal Reasoning / अशाब्दिक तर्क, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Syllogisms / न्यायवाक्य, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Alphabet and Number Test / वर्णमाला एवं संख्या परीक्षण, Statement-Based Reasoning / कथन आधारित तार्किक विवेचन, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी
  4. General Knowledge / सामान्य ज्ञान: Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Chemistry / रसायन विज्ञान, Biology / जीव विज्ञान, History / इतिहास, Geography / भूगोल, Polity / राजव्यवस्था, Indian Economy / भारतीय अर्थव्यवस्था, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान
  5. Art of Teaching / शिक्षण कला: Teaching-Learning Process and Classroom Management / शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन, Learners & Learning Process / अधिगमकर्ता और अधिगम प्रक्रिया, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Teaching Methods and Approaches / शिक्षण विधियाँ एवं उपागम, Microteaching and Classroom Communication / सूक्ष्म शिक्षण एवं कक्षा संप्रेषण, Teaching Aids and Educational Technology / शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी, Assessment and Evaluation / आकलन एवं मूल्यांकन, Teacher: Qualities, Professional Ethics and Development / शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास, Educational Policies, Acts and Administration / शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन, Curriculum, Arts and Co-curricular Areas / पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र, Guidance and Counselling / निर्देशन एवं परामर्श, Education of Children with Disabilities / दिव्यांग बच्चों की शिक्षा, Micro-Teaching & Teaching Skills / सूक्ष्म शिक्षण और शिक्षण कौशल, Lesson Planning / पाठ योजना
  6. Environmental Science / पर्यावरण विज्ञान: Environment / पर्यावरण
  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, 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):
  26. Full Length Mock Test – General + Computer Science:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive tutorial on number theory concepts, specifically focusing on finding the product of factors and divisors for any given integer. The lesson begins by defining fundamental terms such as factors, divisors, and prime factorization, establishing the notation N = p^a * q^b * r^c. The instructor systematically presents key formulas, including the method for calculating the total number of factors as (a+1)(b+1)(c+1) and the specific formula for the product of all factors, which is N^(n/2), where n represents the total count of factors. The video transitions from theoretical definitions to practical application, demonstrating how to solve complex problems involving large numbers like 7056 and smaller integers like 12 and 72. Through step-by-step breakdowns, the instructor illustrates how to identify perfect squares, perform prime factorization, and manipulate exponents to express products in specific forms like (8P)^(4Q) or 2^a * 3^b. The content is structured to guide students from basic definitions through intermediate problem-solving techniques to advanced algebraic manipulations required for competitive exam questions.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a clear definition of factors and divisors, explaining that these are numbers which divide a given number N completely without remainder. The instructor introduces the standard prime factorization notation N = p^a * q^b * r^c and lists essential formulas on the slide. Key visible text includes 'Number of Factors/Divisors' and the formula for counting factors: (a+1)(b+1)(c+1). The instructor also highlights the formula for the product of factors as N^(No. of factors/2). This section establishes the theoretical foundation required for solving subsequent numerical problems, emphasizing the distinction between unique prime factors and total factors.

  2. 2:00 – 5:00 02:00-05:00

    The instructor applies the previously defined formulas to concrete examples, starting with the number 12. The slide displays 'Factors of a number N refers to all the numbers which divide N completely' alongside the list {1, 2, 3, 4, 6, 12}. The lesson then transitions to more complex problems, introducing a question about the product of factors for 7056 represented as (8P)^(4Q). Another problem asks for the sum of exponents when divisors of 72 are multiplied. The instructor begins analyzing 7056, identifying it as a perfect square (84^2) and starting the prime factorization process by breaking 84 into its components, specifically noting '2x42' on the screen.

  3. 5:00 – 10:00 05:00-10:00

    The core of the lesson involves solving the problem for 7056. The instructor demonstrates that 7056 = (84)^2 and factors 84 into 2^2 * 3 * 7, leading to the prime factorization (2^2 * 3 * 7)^2. Using the formula for the number of factors, (4+1)(2+1)(2+1), the total count is calculated as 45. The product of factors formula N^(n/2) is then applied, resulting in (7056)^(45/2), which simplifies to ((84)^2)^(45/2) or (84)^45. The instructor matches this result to the form (8P)^(4Q). Subsequently, a second problem regarding 72 is solved by finding its prime factorization as 2^3 * 3^2, calculating the total factors as (3+1)(2+1) = 12, and applying the product formula to get 72^6.

  4. 10:00 – 10:09 10:00-10:09

    The video concludes with the final steps of solving the problem for 72. The instructor expands the expression (72)^(12/2) into prime bases to find the exponents 'a' and 'b'. The screen shows the calculation leading to a = 18 and b = 12. The final answer is derived by summing these exponents, a + b. This section reinforces the method of expressing products of divisors in the form 2^a * 3^b and calculating the sum of exponents, providing a complete example of the techniques taught throughout the lecture.

The video effectively bridges theoretical number theory concepts with practical problem-solving strategies. The progression from defining factors to applying the product formula N^(n/2) is logical and well-supported by visual aids. The use of 7056 as a perfect square example demonstrates the importance of recognizing number properties to simplify calculations. Similarly, the 72 problem reinforces the method for handling non-perfect squares and expressing results in prime base forms. The consistent use of on-screen text for formulas like (a+1)(b+1)(c+1) ensures clarity. Students should note that the product of factors formula relies heavily on accurate prime factorization and correct exponent counting. The final examples show how to manipulate these results into specific algebraic forms required by exam questions.

Loading lesson…