Tricks To Find Sum of Factors & Sum of Odd & Even Factors

Duration: 13 min

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Module outline

  1. Quantitative Aptitude: Number System, Divisibility Rules, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Partnership, Age Problems, Time and Work, Pipe and Cistern, Speed Time and Distance, Algebra, Arithmetic, Data Interpretation, Sequence and Series (Series), Logarithm, Powers and Exponents (Surds and Indices), Permutation and Combination, Probability, Speed Mathematics and Basic Mathematics, Trigonometry
  2. Logical Reasoning: Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Syllogisms, Inequality, Data Sufficiency, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Venn Diagram, Logical Sequence Of Words, Calendar, Clock, Cubes & Dices, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Noun, Pronoun, Adjectives, Verb, Adverb, Tenses, Subject Verb Agreement (Verb Noun Agreement), Articles, Preposition, Conjunction, Modals, Determiner, Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Construction
  4. Data Structures (Domain Test): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  5. Algorithms (Domain Test): Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms
  6. OOPs (Domain Test): Object Oriented Programming (OOPS)
  7. DBMS (Domain Test): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  8. SQL (Domain Test): SQL
  9. Operating Systems (Domain Test): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  10. Computer Networks (Domain Test): Introduction to CN, Data Communication, 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, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  11. Coding: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  12. Written English Test: English Writing Ability
  13. Psychometric Test: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a mathematics lecture on number systems, specifically focusing on the sum of factors. The instructor begins by introducing the topic with a title slide and then transitions to a whiteboard presentation. The core of the lesson is the derivation and application of a formula to calculate the sum of all factors of a given number. Using the number 60 as a primary example, the instructor first lists all its factors and sums them to get 168. He then demonstrates the prime factorization of 60 as 2^2 * 3^1 * 5^1. The main formula is presented: for a number N = X^a * Y^b * Z^c, the sum of its factors is [(X^(a+1) - 1)/(X - 1)] * [(Y^(b+1) - 1)/(Y - 1)] * [(Z^(c+1) - 1)/(Z - 1)]. The instructor applies this formula to 60, showing the calculation step-by-step to arrive at 168. The lesson then extends to finding the sum of odd and even factors. For the sum of odd factors, the formula is applied by excluding the prime factor 2, resulting in (3^2 - 1)/(3 - 1) * (5^2 - 1)/(5 - 1) = 24. For the sum of even factors, the instructor subtracts the sum of odd factors from the total sum of factors (168 - 24 = 144), or alternatively, factors out 2^1 from the total sum. The video concludes with a thank you message.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video starts with a title slide for 'NUMBER SYSTEM' and then transitions to a presentation slide with the same title, featuring a colorful background with mathematical symbols. The instructor, Yash Jain, appears in a small window in the bottom right corner. The slide includes the text 'The mysterious world of numbers...' and 'Basic To Advance'. The instructor introduces the topic of the number system, specifically focusing on the sum of factors, and begins to write the number 60 on the whiteboard.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues the lesson on the 'Sum of Factors'. He lists all the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, and sums them to get 168. He then shows the prime factorization of 60 as 2^2 * 3^1 * 5^1. The instructor begins to write the general formula for the sum of factors of a number N = X^a * Y^b * Z^c, which is [(X^(a+1) - 1)/(X - 1)] * [(Y^(b+1) - 1)/(Y - 1)] * [(Z^(c+1) - 1)/(Z - 1)]. He explains that this formula is derived from the sum of a geometric series.

  3. 5:00 – 10:00 05:00-10:00

    The instructor applies the formula to the number 60. He substitutes the values into the formula: [(2^(2+1) - 1)/(2 - 1)] * [(3^(1+1) - 1)/(3 - 1)] * [(5^(1+1) - 1)/(5 - 1)]. He calculates each part: (8 - 1)/1 = 7, (9 - 1)/2 = 4, and (25 - 1)/4 = 6. He multiplies these results (7 * 4 * 6) to get 168, confirming the sum of factors. He then explains that the sum of odd factors can be found by excluding the prime factor 2, so the formula becomes (3^2 - 1)/(3 - 1) * (5^2 - 1)/(5 - 1) = 4 * 6 = 24. He also shows that the sum of even factors is the total sum minus the sum of odd factors: 168 - 24 = 144.

  4. 10:00 – 13:26 10:00-13:26

    The instructor concludes the lesson by summarizing the key points. He reiterates the formula for the sum of factors and its application to find the sum of odd and even factors. He emphasizes that the sum of even factors can be calculated by subtracting the sum of odd factors from the total sum of factors. The video ends with a 'Thank You for Watching' message in a neon-style graphic.

The video provides a clear, step-by-step tutorial on calculating the sum of factors of a number. It begins with a practical example, listing all factors of 60 and summing them. It then introduces the general formula derived from the sum of a geometric series, which is the most efficient method for larger numbers. The instructor demonstrates the formula's application to the same example, confirming the result. The lesson is extended to find the sum of odd and even factors, showing two methods: one by directly applying the formula to the relevant prime factors and another by using the relationship between the total sum and the sum of odd factors. This structured approach effectively teaches the concept and its applications.

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