Short Trick to find HCF of Big Numbers

Duration: 10 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. Child Development and Pedagogy / बाल विकास एवं शिक्षाशास्त्र: Concept of Development / विकास की अवधारणा, Psychological Theories of Development / विकास के मनोवैज्ञानिक सिद्धांत, Individual Differences, Personality and Gender / व्यक्तिगत भिन्नताएँ, व्यक्तित्व एवं जेंडर, Intelligence and Creativity / बुद्धि एवं सृजनात्मकता, Learning and Its Theories / अधिगम एवं इसके सिद्धांत, How Children Think and Learn / बालक कैसे सोचते एवं सीखते हैं, Emotion, Motivation, Mental Health and Guidance / संवेग, अभिप्रेरणा, मानसिक स्वास्थ्य एवं निर्देशन, Inclusive Education / समावेशी शिक्षा, Teaching-Learning Process / शिक्षण-अधिगम प्रक्रिया, Teaching Methods and Strategies / शिक्षण विधियाँ एवं रणनीतियाँ, Assessment and Evaluation / आकलन एवं मूल्यांकन, Curriculum and School Activities / पाठ्यचर्या और विद्यालयी गतिविधियाँ, Lesson Planning and Teaching Skills / पाठ योजना और शिक्षण कौशल, Teaching Resources and Educational Technology / शिक्षण संसाधन और शैक्षिक प्रौद्योगिकी, Educational Thinkers, Aims and National Policies / शैक्षिक विचारक, उद्देश्य एवं राष्ट्रीय नीतियाँ, Classroom Management and Communication / कक्षा प्रबंधन और सम्प्रेषण, Teacher Identity and Professional Development / शिक्षक पहचान और व्यावसायिक विकास, Social Science Pedagogy / सामाजिक विज्ञान शिक्षणशास्त्र, Social and Political Life / सामाजिक एवं राजनीतिक जीवन, Science Pedagogy / विज्ञान शिक्षण शास्त्र, Life Skills, Values, Peace and Environmental Education / जीवन कौशल, मूल्य, शांति एवं पर्यावरण शिक्षा, Constitution, Commissions, Acts and Schemes in Education / संविधान, आयोग, अधिनियम एवं योजनाएँ
  2. Mathematics / गणित: Number System & Place Value / संख्या पद्धति एवं स्थानीय मान, Basic Operations, Simplification & Patterns / मूलभूत संक्रियाएँ, सरलीकरण एवं पैटर्न, Factors, Divisibility, HCF & LCM / गुणनखंड, विभाज्यता, म.स.प. एवं ल.स.प., Fractions & Decimals / भिन्न एवं दशमलव, Squares, Cubes, Exponents & Surds / वर्ग, घन, घातांक एवं करणी, Measurement: Length, Mass, Capacity, Time & Money / मापन: लंबाई, भार, धारिता, समय एवं मुद्रा, Algebra / बीजगणित, Ratio, Proportion, Average & Ages / अनुपात, समानुपात, औसत एवं आयु, Percentage, Profit–Loss & Interest / प्रतिशत, लाभ-हानि एवं ब्याज, Time & Work and Speed–Distance / समय-कार्य एवं चाल-दूरी, Lines, Angles, Shapes & Coordinates / रेखाएँ, कोण, आकृतियाँ एवं निर्देशांक, Triangles, Quadrilaterals, Circles & Trigonometry / त्रिभुज, चतुर्भुज, वृत्त एवं त्रिकोणमिति, Mensuration: Perimeter, Area & Volume / क्षेत्रमिति: परिमाप, क्षेत्रफल एवं आयतन, Data Handling, Statistics & Probability / आँकड़ा प्रबंधन, सांख्यिकी एवं प्रायिकता, Mathematics Pedagogy / गणित शिक्षणशास्त्र, Alphabet & Number Test / वर्णमाला एवं संख्या परीक्षण, Non-Verbal Reasoning / अशाब्दिक तर्क, Dice & Cubes / पासा एवं घन, Mathematical Operations & Arithmetical Reasoning / गणितीय संक्रियाएँ एवं अंकगणितीय तर्क, Ranking, Seating Arrangement & Puzzles / क्रम, बैठक व्यवस्था एवं पहेली, Calendar & Clock / कैलेंडर एवं घड़ी, Venn Diagrams & Logical Deduction / वेन आरेख एवं तार्किक निगमन
  3. Environmental Studies / पर्यावरण अध्ययन: Family, Friends and Community / परिवार, मित्र और समुदाय, Plants / पौधे, Animals / जंतु, Farming and Animal Husbandry / खेती और पशुपालन, Food and Nutrition / भोजन और पोषण, Body and Health / शरीर और स्वास्थ्य, Water / जल, Shelter / आवास, Travel, Transport and Communication / यात्रा, परिवहन और संचार, Maps, Directions and India / मानचित्र, दिशाएँ और भारत, Things We Make and Do / हम क्या बनाते और करते हैं, Earth, Sky and Disasters / पृथ्वी, आकाश और आपदाएँ, Environment, Ecology and Wildlife / पर्यावरण, पारिस्थितिकी और वन्यजीव, Natural Resources, Pollution and Climate Change / प्राकृतिक संसाधन, प्रदूषण और जलवायु परिवर्तन, Pedagogy of Environmental Studies / पर्यावरण अध्ययन का शिक्षणशास्त्र, Physical Geography / भौतिक भूगोल, Resources and Development / संसाधन एवं विकास, Force, Pressure, Work and Energy / बल, दाब, कार्य एवं ऊर्जा, Environment and Ecology / पर्यावरण एवं पारिस्थितिकी, Science & Technology / विज्ञान एवं प्रौद्योगिकी, Heat and Sound / ऊष्मा एवं ध्वनि, Light / प्रकाश, Universe and Natural Phenomena / ब्रह्मांड एवं प्राकृतिक परिघटनाएँ, Chemical Reactions, Acids, Bases and Salts / रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण, Natural Vegetation, Wildlife and World Regions / प्राकृतिक वनस्पति, वन्य जीवन एवं विश्व के प्रदेश, Environment & Climate Affairs / पर्यावरण एवं जलवायु समसामयिकी
  4. Language I/II — हिंदी / Hindi: भाषा, लिपि और वर्ण-विचार, संधि, शब्द-स्रोत और शब्द-रचना, समास, शब्द-भेद: विकारी और अविकारी, लिंग, वचन, कारक, काल और वाच्य, वाक्य-विचार और शुद्ध लेखन, शब्द-भंडार, रस, छंद, अलंकार और शब्द-शक्ति, हिंदी साहित्य, अपठित बोध, हिंदी शिक्षणशास्त्र
  5. Language I/II — English: Sounds, Spelling and Word Formation, Parts of Speech, Nouns and Pronouns, Articles, Determiners and Adjectives, Verbs and Modals, Tenses and Subject–Verb Agreement, Adverbs, Prepositions and Conjunctions, Sentence Structure, Voice and Narration, Vocabulary, Sentence Correction and Writing Skills, Poetry and English Literature, Reading Comprehension, Pedagogy of English Language
  6. Language I/II — संस्कृत / Sanskrit: वर्णविचारः एवं संज्ञाप्रकरणम्, सन्धिप्रकरणम्, शब्दरूपाणि, धातुरूपाणि, कारकाणि एवं विभक्तयः, उपसर्गाः एवं अव्ययानि, प्रत्ययप्रकरणम्, समासप्रकरणम्, वाच्यप्रकरणम्, संख्याज्ञानम्, शब्दज्ञानम् एवं अनुवादः, अपठितावबोधनम्, संस्कृतसाहित्यम् एवं काव्यशास्त्रम्, संस्कृतशिक्षणशास्त्रम्
  7. Language I/II — اردو / Urdu: رسم الخط، املا اور تلفظ, ذخیرۂ الفاظ, قواعد, محاورے اور ضرب الامثال, شعر و سخن, اردو ادب کی تاریخ, تفہیمِ عبارت, اردو کی تدریس
  8. Language I/II — বাংলা / Bengali: ভাষা, ধ্বনি ও বর্ণ, সন্ধি ও বানান, শব্দের উৎস ও গঠন, সমাস, পদ পরিচয়, কারক ও বিভক্তি, ক্রিয়া ও কাল, বাক্যতত্ত্ব, শব্দার্থ ও বাগর্থ, পাঠ অনুধাবন ও সাহিত্য, নির্মিতি ও পত্রলিখন, বাংলা শিক্ষণবিদ্যা
  9. Extra Practice (beyond syllabus) / अतिरिक्त अभ्यास (पाठ्यक्रम से बाहर): Computer Hardware and Peripherals / कंप्यूटर हार्डवेयर एवं परिधीय उपकरण, International Relations & Organisations / अंतरराष्ट्रीय संबंध एवं संगठन, Indian Economy: Data & Current Affairs / भारतीय अर्थव्यवस्था: आँकड़े एवं समसामयिकी
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain from Knowledge Gate Eduventures, provides a comprehensive tutorial on finding the Highest Common Factor (HCF) of large numbers. The video begins with an introduction to the topic, defining HCF and explaining its relationship with LCM. The core of the lesson focuses on a practical method for simplifying the calculation of HCF for large numbers by first dividing all numbers by a common factor, typically 10, to reduce them to smaller, more manageable values. This is demonstrated with the example HCF(750, 6300, 18900), where the numbers are divided by 10 to get 75, 630, and 1890. The video then applies the standard prime factorization method to these reduced numbers, showing the step-by-step process of dividing by common prime factors (2, 3, 5) until the numbers are co-prime. The final HCF of the reduced numbers is calculated as 15. The video concludes by multiplying this result by the initial common factor (10) to obtain the correct HCF of the original large numbers, which is 150. The lesson is reinforced with a second example, HCF(108, 288, 360), which is simplified by dividing by 2 to get 54, 144, and 180, and then further reduced to 27, 72, and 90, and so on, to find the HCF of 36. The video uses a digital whiteboard for all calculations and includes a copyright notice.

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 classroom setting with a cartoon teacher and a live instructor, Yash Jain. The topic is introduced as 'Highest Common Common Factor (HCF)'. The instructor explains that the video will cover the HCF of big numbers, setting the stage for the main lesson.

  2. 2:00 – 5:00 02:00-05:00

    The instructor presents the first example: HCF(750, 6300, 18900). He demonstrates the method of simplifying the problem by dividing all three numbers by 10, as they are all divisible by 10. This reduces the problem to finding HCF(75, 630, 1890). He then begins the prime factorization process on the reduced numbers, starting by dividing by 2, 3, and 5, and writing down the resulting quotients.

  3. 5:00 – 10:00 05:00-10:00

    The instructor continues the prime factorization for HCF(75, 630, 1890). He divides the numbers by 3, then by 5, and then by 3 again, showing the step-by-step reduction. The process reveals that the common factors are 3 and 5, and the final co-prime numbers are 1, 1, and 1. He calculates the HCF of the reduced numbers as 3 x 5 = 15. He then multiplies this result by the initial common factor of 10 to get the final answer: 15 x 10 = 150. He confirms this is the correct HCF of the original large numbers.

  4. 10:00 – 10:21 10:00-10:21

    The video presents a second example: HCF(108, 288, 360). The instructor begins by dividing all numbers by 2, resulting in 54, 144, and 180. He continues the process, dividing by 2 again to get 27, 72, and 90. He then divides by 3 to get 9, 24, and 30, and continues to find the HCF of these numbers. The video ends with a 'THANKS FOR WATCHING' screen.

The video provides a clear, step-by-step guide on how to find the HCF of large numbers by first simplifying the problem. The central concept is that if all numbers in a set are divisible by a common factor, the HCF of the original numbers can be found by first dividing all numbers by that common factor, calculating the HCF of the resulting smaller numbers, and then multiplying the result by the initial common factor. This method is demonstrated effectively with two examples, showing the reduction of large numbers to manageable ones through division by common factors (10 and 2), followed by the standard prime factorization technique to find the HCF of the simplified set. The final answer is obtained by reversing the initial simplification step.

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