Short Trick to find HCF by using smallest element

Duration: 10 min

This video lesson is available to enrolled students.

Return to /learn/UPPSC-COMPUTER-OPERATOR-GRADE-B/reasoning/hcf-lcm/finding-hcf/asset-short-trick-to-find-hcf-by-using-smallest-element after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. English Comprehension: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Reading Comprehension, Vocabulary, Idioms and Phrases, Narrative Sequencing, Critical Reasoning
  2. Reasoning and Aptitude: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Seating Arrangements, Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Sufficiency, Selection Decision Table (Decision Making), Calendar, Clock, Cubes & Dices, Data Arrangement, Venn Diagram, Analytical Reasoning (Counting Figures Reasoning), Number System, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Speed Time and Distance, Mensuration and Geometry, Arithmetic, Mixture and Alligation, Age Problems, Data Interpretation, Alphabet and Word Tests, Numerical Reasoning, Number System, Averages, Mixtures and Alligation, Percentages, Series Completion, Analogy and Classification, Patterns in Two-Dimensional Figures, Coding and Decoding, Mathematical Operations, Direction Sense, Logical Deduction and Induction, Simplification and Approximation, Assembling and Grouping of Shapes, Transformation of Shapes, Three-Dimensional Patterns and Visualization, Cubes and Dice, Algebra, Traverse Surveying, Clocks and Calendars, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Ratio and Proportion, Mensuration, Permutations and Combinations, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Sequences and Series, Powers, Surds and Logarithms, Subject-Verb Agreement, Sentence Completion, Geometry, Probability, Trigonometry, Measurement and Quantity Take-Off, Statistics, Data Sufficiency, Blood Relations, Speed, Time and Distance, Time and Work, Data Interpretation, Sequence and Series (Series), Algebra, Permutation and Combination, Combinatorics
  3. General Awareness: Physics, Chemistry, Biology, Geography, History, Polity, Indian Economy
  4. Computer Fundamentals: Basics of COA, Number System, Number Representation, Semiconductor Memories and Programmable Logic, Timing, Hazards and Testing, Processor Organization and Instructions, Number Systems and Codes, Combinational Logic Design, Combinational Logic Circuits, Number Systems and Codes
  5. Operating System: Introduction to OS, Unix OS, Linux OS
  6. C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  7. OOPS with C++ & Java: OOPS with C++, Java
  8. Database Management System: Basics of DBMS, SQL
  9. MS Office: MS Office Applications
  10. Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a step-by-step tutorial on calculating the Highest Common Factor (HCF) using the 'Least Number' method, which is a variation of the prime factorization technique. The instructor, Yash Jain, begins by introducing the topic and then demonstrates the method with several examples. The first example involves finding the HCF of 6, 12, and 18. The method involves identifying the smallest number among the given numbers (the 'pivot element') and then checking if it divides all other numbers. If it does, it is the HCF. If not, the process is repeated with the next smallest number. The video then applies this method to more complex sets of numbers, such as (8, 16, 20, 28, 44) and (8, 11, 16, 20, 28, 44, 46), consistently demonstrating the process of elimination to find the highest common factor. The video concludes with a final example and 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 background. It then transitions to a lecture slide with a green chalkboard background. The slide is titled '5. HCF using Least Number' and presents the first example: 'HCF (6, 12, 18)'. The instructor, Yash Jain, begins to explain the method, writing the numbers 6, 12, and 18 on the board. He identifies 6 as the smallest number and the 'pivot element' for the method, explaining that the goal is to find the highest common factor by checking divisibility.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues the first example, demonstrating the 'Least Number' method. He writes '6, 12, 18' and circles the number 6, labeling it the 'pivot element'. He then checks if 6 divides 12 and 18. He writes '6/12 = 2' and '6/18 = 3', indicating that 6 divides both numbers. Since 6 divides all the numbers in the set, he concludes that the HCF is 6, writing 'HCF = 6'. The video then moves to the next example, 'HCF (8, 16, 20, 28, 44)'. He identifies 8 as the pivot element and checks if it divides all other numbers. He writes '8/16 = 2', '8/20 = 2.5', and '8/28 = 3.5', showing that 8 does not divide 20 or 28. He then circles 8 and marks the other numbers with a cross, indicating they are not divisible by 8. He then identifies the next smallest number, 16, as the new pivot element and begins to check its divisibility.

  3. 5:00 – 9:34 05:00-09:34

    The instructor continues with the second example, 'HCF (8, 16, 20, 28, 44)'. He checks if 16 divides 8, 20, 28, and 44, and finds that it does not. He then moves to the next smallest number, 20, and checks its divisibility, finding it fails. He continues this process, checking 28 and 44, all of which fail. He then identifies 4 as a common factor and checks if it divides all numbers, finding that it does. He concludes that the HCF is 4. The video then presents a third example: 'HCF (8, 11, 16, 20, 28, 44, 46)'. He identifies 8 as the pivot element and checks divisibility, finding it fails for 11, 16, 20, 28, 44, and 46. He then checks 11, which fails for 8, 16, 20, 28, 44, and 46. He continues this process, eventually finding that 2 is the only number that divides all the numbers in the set. He concludes that the HCF is 2. The video ends with a 'Thanks for Watching' screen.

The video systematically teaches a specific method for finding the Highest Common Factor (HCF) by using the 'Least Number' approach. The core concept is to start with the smallest number in the set and test if it is a common divisor for all other numbers. If it is, it is the HCF. If not, the process is repeated with the next smallest number until a common divisor is found. This method is demonstrated through three distinct examples, each increasing in complexity, to reinforce the concept. The video effectively uses on-screen writing and clear verbal explanation to guide the viewer through the logical steps of the algorithm, making it a practical tutorial for students learning about HCF.

Loading lesson…