Class 10 Maths — Chapter 1: REAL NUMBERS

Chapter 1: REAL NUMBERS is a chapter in Class 10 Maths (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 7 topics including The Fundamental Theorem of Arithmetic, Prime Factorization Method, HCF by Prime Factorization. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.

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What you'll learn

▸The Fundamental Theorem of ArithmeticCore concept

Fundamental Theoremunique factorizationcomposite numberproduct of primes
▸Prime Factorization MethodCore concept

prime factorsfactor treeexpress as productpowers of primes
▸HCF by Prime FactorizationCore concept

HCFHighest Common Factorcommon prime factorsmallest power
▸LCM by Prime FactorizationCore concept

LCMLeast Common Multipleprime factorgreatest power
▸HCF and LCM Product RuleCore concept

HCF x LCMproduct of numbersverify relationshipformula
▸Divisibility and End Digits

ends with zerodigit 0divisibility6^nprime factors
▸Identifying Composite Numbers

composite numbersexplain whycommon factorprime number

Chapter Summary

Understand the core statement that every composite number can be factorized as a product of primes, and this factorization is unique, apart from the order of the prime factors.

Learn to express any given integer as a product of its prime factors, typically using a factor tree, and write it in exponential form (e.g., 360 = 2³ × 3² × 5).

Calculate the Highest Common Factor (HCF) of two or more integers by finding the product of the smallest power of each common prime factor in the numbers.

Calculate the Least Common Multiple (LCM) of two or more integers by finding the product of the greatest power of each prime factor involved in the numbers.

Understand and apply the relationship for any two positive integers 'a' and 'b': HCF(a, b) × LCM(a, b) = a × b. Use this formula to find a missing HCF, LCM, or number.

Apply the uniqueness of the Fundamental Theorem of Arithmetic to determine properties of numbers, for instance, checking if a number of the form 4ⁿ or 6ⁿ can end with the digit zero by analyzing its prime factors.

Learn to prove that a number is composite by showing it has factors other than 1 and itself, often by simplifying expressions like '7 × 11 × 13 + 13' to show a common factor.

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

Explain prime factorization simply. Get Solution →
Show a factor tree example. Get Solution →
Name real-world uses for primes. Get Solution →
What does the Fundamental Theorem of Arithmetic state? Get Solution →
According to the text, who is credited with giving the first correct proof of the Fundamental Theorem of Arithmetic? Get Solution →
The prime factorization of a natural number is unique, except for what? Get Solution →
How is the HCF of two positive integers found using the prime factorization method? Get Solution →
For any two positive integers a and b, what is the relationship between their product and their HCF and LCM? Get Solution →

Did you know?

💡 The number zero was invented independently by several ancient cultures.
💡 There is only one even prime number, and that number is two.
💡 Mathematicians still discover new, larger prime numbers regularly.
💡 Ancient Egyptians used only fractions with a numerator of one.
💡 Computers use prime numbers to create strong, secret codes.

Frequently Asked Questions

How many topics are covered in this chapter?

This chapter covers 7 key topics: The Fundamental Theorem of Arithmetic, Prime Factorization Method, HCF by Prime Factorization, LCM by Prime Factorization, HCF and LCM Product Rule, and more. The BrainWeave AI tutor explains each one with examples.

Is Chapter 1: REAL NUMBERS important for board exams?

Yes — Class 10 is a CBSE board exam year, and every NCERT chapter is part of the syllabus. Use BrainWeave's AI tutor to master this chapter, then practice with the auto-generated quizzes and mind maps.

Can I get NCERT solutions for this chapter in Hindi?

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Is BrainWeave free for Class 10?

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Related Chapters

Chapter 2: POLYNOMIALS

Chapter 10: CIRCLES

Chapter 6: TRIANGLES

Chapter 13: STATISTICS

Chapter 8: TRIGONOMETRY

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