Fundamental Theorem of Arithmetic | Prime Factorization | Factor Tree | Number Theory | BSc 1st Year

Описание: Fundamental Theorem of Arithmetic | Prime Factorization | Factor Tree | Number Theory | BSc 1st Year


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Welcome to K.Mathematics 🎓


In this lecture, we discuss the Fundamental Theorem of Arithmetic, one of the most important results in Number Theory, for BSc 1st Year Mathematics students studying Introduction to Algebra and Number Theory.

This video explains how every integer greater than 1 can be written as a product of prime numbers and why this factorization is unique. We also cover Euclid’s Lemma, its extension, Prime Factorization (Canonical Decomposition), the Factor Tree Method, and how to find all factors of a number using prime factorization.

This lecture is explained step-by-step in a simple and exam-oriented way for BSc students and mathematics learners.


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✅ Topics Covered

✔ Euclid’s Lemma (Statement & Proof)
✔ Extension of Euclid’s Lemma
✔ Fundamental Theorem of Arithmetic (Existence & Uniqueness)
✔ Prime Factorization / Canonical Decomposition
✔ Factor Tree Method
✔ Finding All Factors Using Prime Factorization


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⏱️ Timestamps

00:00 — Introduction
00:42 — Euclid’s Lemma
02:40 — Extension of Euclid’s Lemma
05:10 — Fundamental Theorem of Arithmetic
13:10 — Prime Factorization / Canonical Decomposition
15:48 — Factor Tree Method
17:30 — Finding Factors Using Prime Factorization
21:14 — Outro


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🎯 Who Should Watch This Video

✅ BSc 1st Year Mathematics Students
✅ Introduction to Algebra and Number Theory Course
✅ Competitive Exam Preparation (CSIR NET / IIT JAM Basics)
✅ Students Learning Number Theory Fundamentals


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📚 Course: Introduction to Algebra and Number Theory

🎓 Level: BSc 1st Year Mathematics

📺 Channel: k.mathematics


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