IIT Foundation Mathematics - Number Systems-The number of divisors of 72 is - WS-5

IIT Foundation Mathematics - Number Systems-The number of divisors of 72 is - WS-5 📘 What is The Number of Divisors? The number of divisors of a natural number refers to how many positive integers can divide that number exactly — meaning without leaving any remainder. For example, if we take the number 12, its divisors are: 1, 2, 3, 4, 6, and 12. So, the number of divisors of 12 is 6. 🔍 How Do We Find The Number of Divisors? To find the number of divisors of a number quickly (especially when the number is large), we use prime factorization. Step-by-step method: Find the prime factorization of the number. For example: 36 = 2² × 3² Add 1 to each exponent, then multiply the results. For 36: (2 + 1)(2 + 1) = 3 × 3 = 9 So, the number of divisors of 36 is 9. These 9 divisors are: 1, 2, 3, 4, 6, 9, 12, 18, and 36. This method helps us calculate the number of divisors without listing them all, which saves time in exams. 🧠 Important Notes: If a number is prime, then the number of divisors is always 2 (1 and the number itself). If a number is a perfect square, then the number of divisors is odd. (Because one of the divisors is repeated. For example, 36 has 9 divisors.) If two numbers are coprime, then the number of divisors of their product can be found by multiplying the number of divisors of each. 🤔 Why is This Important? Understanding the number of divisors helps in solving many types of questions in: Factor and Multiple problems Number systems LCM and HCF Geometry (like counting edges/faces in 3D shapes) And even in higher-level topics like permutations and probability! Learning how to find the number of divisors efficiently builds a strong foundation for JEE and other competitive exams. Welcome to Kaal Gyaan Academy – your trusted guide for IIT Foundation Mathematics! In this video, we dive deep into the Number Systems, one of the most fundamental and crucial topics for students preparing for IIT JEE, NTSE, Olympiads, and school exams (CBSE/ICSE/State Boards). Whether you're in this session will build your conceptual clarity and give you a solid base for advanced problem-solving in higher classes. A strong understanding of number systems is essential for cracking competitive exams like JEE Main, JEE Advanced, and other engineering entrance tests. 🔢 What You'll Learn in This Video: ✔️ Natural Numbers, Whole Numbers, Integers ✔️ Rational and Irrational Numbers ✔️ Real Numbers and Their Properties ✔️ Prime and Composite Numbers ✔️ Divisibility Rules and Shortcuts ✔️ LCM and HCF – Concept and Tricks ✔️ Important Theorems: Euclid’s Lemma, Fundamental Theorem of Arithmetic ✔️ Number Line Representation ✔️ Surds and Decimals ✔️ Solved Examples and Practice Questions 🎯 Why This Video is Important: Building a strong foundation in mathematics is critical for early IIT JEE preparation. This chapter helps you understand how numbers work, which forms the base for algebra, geometry, and advanced arithmetic. It’s also one of the most scoring topics in school and competitive exams. 🌟 Who Should Watch This Video: 🔸 IIT-JEE aspirants (Early Starters) 🔸 NTSE / KVPY / Olympiad Participants 🔸 CBSE, ICSE, and State Board Students 🔸 Parents and Teachers looking to guide students better 🧠 Try This! Comment below with your answers to the following challenge question from today’s session: "Find the smallest number which when divided by 12, 18, and 24 leaves a remainder of 6." Let’s see who gets it right! 💬👇 📌 Important Tips for Mastering Number Systems: 🔹 Practice LCM and HCF using real-life examples 🔹 Memorize prime numbers up to 100 🔹 Understand the concept behind divisibility rules 🔹 Use number lines to visualize numbers better 🔹 Revisit irrational numbers and surds with solved questions 👉 New Videos Every Week! Subscribe & Hit the Bell Icon 🔔 🔥 Don’t Forget to Like 👍 | Share ↗ | Subscribe 🔔 🔔 Click here to subscribe: [Your Subscribe Link] 💬 Tell us in the comments what topic you want next! #IITFoundation #NumberSystems #Class9Maths #Class8Maths #MathsForIITJEE #NTSE #OlympiadMaths #HCF #LCM #DivisibilityRules #Mathematics #NumberSystemClass9 #IITFoundationMaths #CBSEMaths #ICSEmaths #Surds #RealNumbers #EarlyJEEPrep #foundationcourses IIT Foundation Mathematics Number System full chapter, Number system for IIT JEE early preparation, How to learn number system for competitive exams, Maths number system for class 8 to 10, Best explanation of number system for JEE, Number system questions for NTSE and Olympiad, Early JEE preparation math topics, IIT Foundation Number Systems for beginners, IT Foundation Mathematics Number Systems IIT JEE Preparation IIT Foundation Course Mathematics for IIT JEE Real Numbers Class 10 Number System Tricks Number System Basics Number System for NTSE Number System Olympiad