An Important Property of HCF & LCM + Practice Question

Duration: 13 min

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Module outline

  1. 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, Relational Calculus, Transaction Management, Concurrency Control
  2. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Virtual Memory, Disc Scheduling, File Management, Memory Management, Threads & Process Creation
  6. Computer Networks: Introduction to CN, 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, Network Security, Hardware Basics
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis
  9. 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, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  11. C language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums
  12. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Emerging Trends & AI: Emerging Tech Trends, Artificial Intelligence, Cloud Computing
  14. Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing
  15. Aptitude: Percentage, Ratio and Proportion (Ratios), Logarithm, HCF LCM, Divisibility Rules, Average, Sequence and Series (Series), Number System, Powers and Exponents (Surds and Indices), Algebra, Permutation and Combination, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Data Interpretation, Arithmetic, Speed Mathematics and Basic Mathematics, TCS NQT Advanced Quantitative Ability, Gamified / Game Based Aptitude, Linear Algebra, Trigonometry
  16. Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), 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
  17. English (Verbal Ability): Vocabulary, Noun, Pronoun, Adjectives, Preposition, Articles, Direct and Indirect Speech, Tenses, Conjunction, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Interjection, Verb, English Writing Ability
  18. Engineering Mathematics: Calculus, Vectors
  19. GATE Live Class Recordings 2026: GATE 2026 Live Class
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lesson on finding the Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD). The lecture begins with an introduction to the topic, defining HCF and establishing a key property: the HCF of a set of numbers is always less than or equal to the smallest number in the set. The instructor then demonstrates the fundamental method of finding the HCF by listing the factors of each number and identifying the largest common factor. This method is applied to the numbers 6, 12, and 18, resulting in an HCF of 6. The video progresses to a more efficient method using prime factorization, which is demonstrated by breaking down the numbers 30, 42, and 135 into their prime factors and multiplying the common prime factors. The final segment presents a multiple-choice question to test the viewer's understanding, where the correct answer is determined to be 3. 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 card displaying 'LCM & HCF' against a digital, data-stream background. It then transitions to a classroom setting with a cartoon teacher and a live instructor. The main topic is introduced as 'Highest Common Common Factor (HCF)'. The instructor, Yash Jain, begins by stating a fundamental property of HCF: 'HCF is always smaller than or equal to the smallest number'. This is written on the screen as a key concept. The video then introduces a worked example with the numbers 6, 12, and 18, setting up the problem HCF(6, 12, 18).

  2. 2:00 – 5:00 02:00-05:00

    The instructor explains the method for finding the HCF by listing the factors of each number. He writes out the factors of 6 as {1, 2, 3, 6}, the factors of 12 as {1, 2, 3, 4, 6, 12}, and the factors of 18 as {1, 2, 3, 6, 9, 18}. He then identifies the common factors (CF) as {1, 2, 3, 6} and concludes that the Highest Common Factor (HCF) is 6. This is visually confirmed with a checkmark next to the answer. The instructor also writes the inequality HCF ≤ 6, reinforcing the earlier rule that the HCF is less than or equal to the smallest number.

  3. 5:00 – 10:00 05:00-10:00

    The video transitions to a new problem: 'Find the GCD of 30, 42, 135?'. The instructor begins to solve this using the prime factorization method. He starts by dividing 30 by 2, getting 15, and then divides 15 by 3, getting 5. He then divides 42 by 2, getting 21, and divides 21 by 3, getting 7. For 135, he divides by 3, getting 45, then by 3 again, getting 15, and finally by 3 again, getting 5. He then writes the prime factorization of each number: 30 = 2 × 3 × 5, 42 = 2 × 3 × 7, and 135 = 3 × 3 × 3 × 5. He identifies the common prime factor, which is 3, and concludes that the GCD is 3. He marks the correct answer (A) as 3 and crosses out the other options.

  4. 10:00 – 12:47 10:00-12:47

    The instructor reviews the solution to the multiple-choice question, confirming that the GCD of 30, 42, and 135 is 3. He shows the prime factorization of each number again, emphasizing that the only common prime factor is 3. The video then displays a 'Thanks for Watching' screen, concluding the lesson. The entire video is presented as a tutorial by Knowledge Gate Eduventures, with a copyright notice visible at the bottom of the screen throughout.

The video provides a clear, step-by-step tutorial on finding the Highest Common Factor (HCF). It begins by establishing a foundational rule that the HCF is always less than or equal to the smallest number. The primary method demonstrated is the factor listing method, which is used to find the HCF of 6, 12, and 18, resulting in 6. The video then introduces the more efficient prime factorization method to solve a more complex problem involving 30, 42, and 135. By breaking down each number into its prime factors, the instructor identifies the common factors and calculates the GCD as 3. The lesson is structured to build from a basic concept to a more advanced application, using worked examples and a multiple-choice question to reinforce learning.

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