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This section gives a glimpse of what students would learn about positive numbers in the later sections of Chapter 1 Maths Class 10, i. 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 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. Rational numbers and irrational numbers are taken together form the set of real numbers. The set of real numbers is denoted by R. Thus every real number is either a rational number or an irrational number. In either case, it has a non�terminating decimal representation. In the case of rational numbers, the decimal representation is repeating including repeating zeroes and if the decimal representation is non�repeating, it is an irrational number.
From the above discussion we may conclude that: To every real number there corresponds a unique point on the number line and conversely, to every point on the number line there corresponds a real number. We have studied the following points: 1. The divisor at this stage will be HCF a, b.
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