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The Fundamental Theorem of Arithmetic is based on the fact that a composite number can be expressed as a product of prime numbers, in distinct ways.
This theorem has deep and significant applications in mathematics. A lemma is a statement that is proven and acts as a stepping stone to prove other statements. A is the quotient. B is the remainder. An algorithm is a set of well-defined steps that can procedurally solve a problem. According to this theorem, every composite number can be factorized as a product of some prime numbers.
It is a unique prime factorization of natural numbers Real Numbers Class 10th Ncert Solutions News as the order of the factors does not matter. We will understand this with an example that is based on the following fundamentals:. HCF - The highest common factor of two or more integers is the greatest integer that can exactly divide all the given integers. For example, HCF of 60 and 75 is LCM - The Least Common Multiple of two or more integers is the smallest integer that is exactly divisible by all the given integers.
For example, LCm of 2, 4, and 5 is In this section of NCERT Solutions for Class 10th Maths Chapter 1, you will remember the definition of Irrational numbers learned in earlier classes and then prove p is an irrational number, where p is a prime number. Few examples of irrational numbers are 2,3, etc. The Class 10 Maths Chapter 1 Solutions are also available for download in a PDF format which makes revisions very quick and easy during stressful exam times. Proof: � Let p be a prime number and a be a positive integer such that p divides We all are aware that every positive integer can be expressed as the product of primes.
Thus, 3 is a common factor of a and b But this contradicts the fact that a and b have no common factors other than 1. Share and Enjoy! No comments, be the first one to comment! Leave a Reply Cancel reply Your email address will not be published. Blog Search Search for:. What is an Operating System? Types of OS, Features, and Examples. All Rights Reserved. Terms and Conditions We are Hiring! Send us a Message. Remember me. Register Create an Account. Powered by Join.
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