Demo: Short Tricks to Find Number of Odd & Even Factors

Duration: 18 min

This video lesson is available to enrolled students.

Return to /learn/BPSC/part-2-primary-maths/number-system-bff2d7/factors-multiples-prime-factorization/asset-demo-short-tricks-to-find-number-of-odd-even-factors after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Section 1 | भाषा (हिंदी) / Language (Hindi): भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, 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, शब्द-भंडार, अपठित बोध, बहुविषयक सामग्री (विभिन्न अवधारणाओं से संबंधित सामग्री), वर्णमाला
  3. Section 1 | اردو زبان / Language (Urdu) — 22 Questions (Fixed): رسم الخط، حروفِ تہجی اور املا, اسم، ضمیر اور صفت, الفاظ، محاورے اور ضرب الامثال, تفہیمِ عبارت، انشا اور ترجمہ, تفہیم
  4. Section 1 | বাংলা ভাষা / Language (Bengali) — 22 Questions (Fixed): শব্দার্থ, বাগধারা ও ভাষাশুদ্ধি, বাক্য ও বাচ্য, শব্দগঠন ও শব্দভান্ডার, অনুবাদ, বোধপরীক্ষণ ও রচনা
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Pronoun, Verb, Adverb, Prepositions and Conjunctions, Parts of Speech, Determiner, Conjunction, Modals, Transformation of Sentences, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Structure and Common Errors, Reading Comprehension, Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning / प्राथमिक गणित एवं तर्कशक्ति: Ratio and Proportion / अनुपात और समानुपात, Divisibility Rules / विभाज्यता के नियम, Mixture and Alligation / मिश्रण और एलिगेशन, Permutation and Combination / क्रमचय और संचय, Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Sequences, Series and Combinatorics / अनुक्रम, श्रेणी और संयोजन, Time, Speed and Distance / समय, चाल और दूरी, Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Non-Verbal Reasoning / अशाब्दिक तर्क, Percentage / प्रतिशत, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Age Problems / आयु संबंधी प्रश्न, Arithmetic / अंकगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Algebra / बीजगणित, Probability / प्रायिकता, Trigonometry / त्रिकोणमिति, Syllogisms / न्यायवाक्य, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी, Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Data Arrangement / आँकड़ों की व्यवस्था, Inequality / असमानता, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Order and Ranking / क्रम एवं रैंकिंग, 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
  7. Section 2 | General Awareness (GK + Current Affairs) / सामान्य जागरूकता (GK + समसामयिकी): Polity / राजव्यवस्था, Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Biology / जीव विज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान, Chemistry / रसायन विज्ञान, History / इतिहास, Geography / भूगोल, Indian Economy / भारतीय अर्थव्यवस्था, Environment / पर्यावरण, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान
  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): Computer Fundamentals, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications, Trade, Marketing and Consumer Protection / व्यापार, विपणन एवं उपभोक्ता संरक्षण, Cyber Safety and Security, Computer Software, Operating System, Computer Networks, Word Processing (MS Word), Terms & Abbreviations, Presentation Software (MS PowerPoint), Internet of Things, Cloud Computing
  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, OOPS with Java
  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 systematic approach to finding the number of odd and even factors for integers, culminating in solving probability problems involving perfect squares and cubes. The instructor begins by introducing a specific problem regarding the factors of 24000, asking for the probability that a randomly chosen factor is a perfect square. To build foundational understanding, he transitions to simpler examples like the number 12 and 24. He explicitly lists all factors for these smaller numbers to visualize the concept before introducing the more efficient method of prime factorization. The core technique involves decomposing a number into its prime power form, such as $N = 2^a imes 3^b$, and applying the divisor counting formula $(a+1)(b+1)$. The lecture distinguishes between total factors, odd factors (derived by ignoring the power of 2), and even factors. The final segment applies these principles to the main problem, calculating the prime factorization of 24000 as $2^6 imes 3^1 imes 5^3$ and determining the probability of selecting a perfect cube factor by analyzing exponent constraints.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a probability problem displayed on screen asking for the likelihood that a factor chosen at random from 24000 is a perfect square. The slide presents four multiple-choice options: (a) 1/4, (b) 1/6, (c) 1/8, and (d) None of these. The instructor gestures while reading the problem statement, emphasizing the target number 24000 and the specific condition of finding a perfect square factor. This initial segment sets the context for applying number theory concepts to probability questions.

  2. 2:00 – 5:00 02:00-05:00

    To explain the underlying logic, the instructor transitions to a simpler example using the number 12. He explicitly lists the factors of 12 as {1, 2, 3, 4, 6, 12} to demonstrate how factors are identified. He then breaks down 12 into its prime factorization form, $N = (2^2 imes 3) / 2$, simplifying it to $2^1 imes 3^1$. The instructor derives the divisor counting rule by showing that for each prime base, one adds 1 to its exponent. He writes out the calculation $(1+1)(1+1) = 4$ to verify the count of factors, visually connecting prime powers like $2^0 imes 3^0 = 1$ to the actual factors.

  3. 5:00 – 10:00 05:00-10:00

    The lesson continues with the prime factorization of 12, written as $N = (2^2 imes 3^1) / 3$, and calculates the total factors using exponents. The instructor then introduces a new example, 24, breaking it down into $2^3 imes 3$. He demonstrates the division method to find factors, listing them as {1, 2, 3, 4, 6, 8, 12, 24}. A key transition occurs as he categorizes these factors into 'odd' and 'even' sets. He highlights that for 12, there are specific counts of odd factors (3) and even factors (4), summing to a total of 6. This section establishes the method for distinguishing between odd and even factors based on prime decomposition.

  4. 10:00 – 15:00 10:00-15:00

    The instructor formalizes the method for calculating odd and even factors using prime factorization. For the number 12 ($2^2 imes 3^1$), he applies the formula $(a+1)(b+1)$ to find total factors. He then analyzes 24 ($2^3 imes 3^1$) to categorize factors into odd, even, and total counts. The visual notes show a table structure with columns for 'odd', 'even', and 'total'. He emphasizes that odd factors are found by ignoring the power of 2 in the prime factorization, while even factors require at least one factor of 2. This systematic breakdown prepares the viewer to handle larger numbers like 24000.

  5. 15:00 – 18:01 15:00-18:01

    In the final segment, the instructor solves the initial probability problem regarding 24000. He performs prime factorization on 24000, resulting in $2^6 imes 3^1 imes 5^3$. He sets up the probability formula $P(E) = ext{favorable} / ext{total}$ and identifies the condition for a factor to be a perfect cube: exponents must be multiples of 3. By analyzing the possible combinations of prime powers that satisfy this condition, he calculates the number of favorable outcomes. The final derived answer is shown on screen as 1/7, contrasting with the initial multiple-choice options.

The lecture effectively bridges the gap between basic factor listing and advanced probability applications through a structured progression of examples. The pedagogical strategy relies on scaffolding: starting with the manual enumeration of factors for small integers like 12 and 24 to build intuition, then introducing the prime factorization formula $(a+1)(b+1)$ for efficiency. A critical conceptual distinction is made between total factors, odd factors (derived by excluding the prime base 2), and even factors. This distinction is essential for solving the final probability problem involving 24000, where the instructor must determine the count of perfect cube factors. The video demonstrates that for a factor to be a perfect cube, its prime exponents must be divisible by 3. By applying this constraint to the factorization $2^6 imes 3^1 imes 5^3$, the instructor calculates the favorable outcomes against the total possible factors. The final result of 1/7 indicates that the probability of selecting a perfect cube factor from 24000 is distinct from the initial options provided, highlighting the importance of rigorous calculation over estimation.

Loading lesson…