# Fundamental Theorem of Arithmetic

State \u0026 Proof of Fundamental Theorem of Arithmetic || Number Theory B.A./B.Sc 1st year maths
State \u0026 Proof of Fundamental Theorem of Arithmetic || Number Theory B.A./B.Sc 1st year maths

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Every composite number can be expressed (factorised) as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur. Ex: 30 = 2×3×5 LCM and HCF: If a and b are two positive integers. Then the product of a, b is equal to the product of their LCM and HCF. LCM×HCF= a × b To Find LCM and HCF of 12 and 18 by the prime factorization method. 12 = 2×2×3 = 2 2 ×3 1 18 =2×3×3= 2×3 2 HCF of 12 and 18 = 2 1 ×3 1 =6 (Product of the smallest powers of each common prime factors in the numbers) LCM of 12 and 18 = 2 2 ×3 2 = 36 (Product of the greatest powers of each prime factors in the numbers) Product of the numbers = 12×18= 216 LCM×HCF = 36×6= 216 Product of the numbers = LCM×HCF • Natural numbers Set N= {1,2,3,4,-} • Whole number Set W ={0,1,2,3,4,-} • Integers z(or) I = {-3,-2,-1, 0, 1, 2, 3,-} Rational numbers (Q): If p, q are whole numbers and q≠0 then the numbers in the form of p q are called Rational numbers. ∴

International Journal of Mathematics Trends and Technology

H.C.F and L.C.M – A Case Study of Completeness Property of Real Numbers

2016 •

A prominent feature of this book is the inclusion of many examples. Each example is carefully selected to illustrate the application of a particular mathematical technique and interpretation of results. Another feature is that each chapter has an extensive collection of exercises. It is important that students have several exercises to practice. This book is therefore designed to help students to: 1. acquire the basic skills and understanding which is vital to examination success. 2. appreciate the use of mathematics as a tool for analysis and effective thinking. 3. discover order, patterns and relations. 4. communicate their thoughts through symbolic expressions and graphs. 5. develop mathematical abilities useful in commerce, industry and public service.

2005 •

the basic engineering of the mathematics

SKE Assignment for ST Mary’s University London