Demo: Short Trick to find HCF by minimum difference method

Duration: 14 min

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Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): 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
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- 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): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  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
  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 demonstrates a specialized technique for calculating the Highest Common Factor (HCF) known as the Minimum Difference Method. The core concept involves finding the difference between two or more numbers and analyzing its factors to determine the HCF. The instructor emphasizes a critical caveat: the minimum difference itself is not always the final answer, as some of its factors may need to be eliminated if they do not divide all original numbers evenly. The lesson progresses from simple two-number examples to more complex three-number scenarios, illustrating how to systematically test prime factors of the difference against the original set. Key steps include calculating differences, performing prime factorization on those differences, and verifying divisibility to isolate the true common factor.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an introduction to the 'Minimum Difference Method' for finding HCF, using 56 and 84 as the primary example. The instructor immediately highlights a crucial theoretical constraint displayed on screen: 'Every time minimum difference will not be the final answer. Some factors of min. difference may be eliminated.' This sets the stage for a method that requires verification rather than simple subtraction. The visual text '4. HCF by Minimum Difference Method' and the problem statement 'HCF (56, 84)' establish the specific topic. The instructor begins by calculating the difference between the two numbers, showing '84 - 56 = 28' on screen. This initial segment focuses on setting up the problem and warning students against assuming the difference is automatically the HCF, preparing them for a factorization process.

  2. 2:00 – 5:00 02:00-05:00

    In this segment, the instructor demonstrates the factorization of the calculated difference (28) to find potential HCFs. The screen displays the prime factorization '28 = 2 x 2 x 7'. The teaching process involves testing these factors against the original numbers (56 and 84) to see if they divide evenly. The instructor notes that factors of the minimum difference may be eliminated, reinforcing the earlier warning. A specific visual cue 'Reserved Words : 2' appears, indicating that certain factors are being set aside or tracked during the process. The instructor explains that while 2 is a factor of both numbers, it might not be the highest common one if other factors like 7 are also present. This section bridges the gap between calculating a difference and rigorously testing its components to find the true HCF.

  3. 5:00 – 10:00 05:00-10:00

    The lesson expands to handle three numbers, introducing the problem 'HCF (15, 39, 153)'. The instructor calculates the differences between pairs of these numbers to identify a minimum difference, which is found to be 24. The screen explicitly shows 'min diff = 24' and its prime factorization '24 = 2x2x2x3'. A critical rule is displayed: 'If all the factors are eliminated, then HCF will be 1', covering cases where numbers share no common factor other than unity. The instructor proceeds to test the factors of 24 against the original numbers (15, 39, 153). This part of the video illustrates how to manage multiple numbers by focusing on the smallest difference and systematically eliminating factors that do not divide all three values, ensuring a robust method for complex sets.

  4. 10:00 – 13:33 10:00-13:33

    The final segment applies the method to a more complex set of three numbers: 'HCF (238, 322, 434)'. The instructor identifies a common difference of 84 and begins factorizing it, showing '84 = 21 x 4' and '84 = 7 x 3 x 2 x 2'. A key technique demonstrated is dividing the original numbers by a common factor (in this case, 2) to simplify the problem, resulting in new values '119, 161, 217'. The instructor then checks for further common factors like 7 and 17 in these reduced numbers. The video concludes with a brief example 'HCF (5, 18)' where the minimum difference is 13, followed by a 'THANKS FOR WATCHING' screen. This section reinforces the iterative nature of the method, showing how to reduce numbers and continue testing factors until the HCF is fully determined.

The video provides a structured approach to finding the Highest Common Factor (HCF) using the Minimum Difference Method, which is particularly useful for numbers that are close in value or have large prime factors. The central thesis is that the difference between numbers contains all potential common factors, but not every factor of the difference will necessarily be a common factor for the entire set. The method requires a two-step verification process: first, calculating the difference and factorizing it into primes; second, testing each prime factor against all original numbers to ensure divisibility. The instructor uses a progression of examples, starting with two numbers (56, 84), moving to three numbers (15, 39, 153), and finally tackling larger values (238, 322, 434). A recurring visual aid is the 'Reserved Words' or tracking of factors like 2, which helps students keep track of common divisors found during the process. The lesson also addresses edge cases, such as when all factors are eliminated, resulting in an HCF of 1. This technique simplifies the search space for common factors compared to traditional prime factorization of all numbers, making it an efficient tool for competitive exams or quick calculations.

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