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Real Numbers Class 10 Notes Maths Chapter 1

Last Updated : 23 Jul, 2025

CBSE Class 10 Maths Notes Chapter 1 Real Numbers are the resource created by the experienced team of Subject Experts at GfG for the benefit of the students. The team at GfG are the well-wishers of students and always put the benefit of students and leaner first and create beneficial content in the form of articles. The result of which are these Notes, which are the comprehensive summary of the completer chapter and includes all the important topics in the chapter. 

Chapter 1 of the CBSE Class 10 Maths is Real Numbers which takes students further in the journey of Real Numbers as previous classes already introduced this topic and cleared the definition. In this chapter, students learn about proof specifically a method of proof that is called proof by contradiction. Other than this, HCF, LCM, Euclid Division Algorithm, and the Fundamental Theorem of Arithmetic are some of the topics which are covered in these notes.

Important Topics in CBSE Notes for Class 10 Chapter 1- Real Numbers 

  • : Euclid’s Division Lemma states if we have two a and b, then there exist unique integers q and r such that a = bq + r, where 0 ≤ r ≤ b. 

Note: Here, a is the dividend, b is the divisor, q is the quotient, and r is the remainder.

  • which tells us that how all the composite number can be factorized 
  • by prime factorizationmethod:
    • HCF (Highest Common Factor) = Product of the smallest power of each common factor in the numbers
    • LCM (Lowest Common Multiple) = Product of the greatest power of each prime factor involved in the number
    • HCF (a,b) × LCM (a,b) = a × b

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