Class 10 Maths — Chapter 1: REAL NUMBERS

What you'll learn

• ▸The Fundamental Theorem of Arithmetic
• ▸Prime Factorization Method
• ▸HCF by Prime Factorization
• ▸LCM by Prime Factorization
• ▸HCF and LCM Product Rule
• ▸Divisibility and End Digits
• ▸Identifying Composite Numbers

Chapter Summary

--- PAGE 1 --- REAL NUMBERS 1 1.1 Introduction In Class IX, you began your exploration of the world of real numbers and encountered irrational numbers. We continue our discussion on real numbers in this chapter. We begin with very important properties of positive integers in Sections 1.2, namely the Euclid’s division algorithm and the Fundamental Theorem of Arithmetic. Euclid’s division algorithm, as the name suggests, has to do with divisibility of integers. Stated simply, it says any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b. Many of you probably recognise this as the usual long division process. Although this result is quite easy to state and understand, it has many applications related to the divisibility properties of integers. We touch upon a few of them, and use it mainly to compute the HCF of two positive integers. The Fundamental Theorem of Arithmetic, on the other hand, has to do someth…

Practice Questions from this Chapter

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1. Explain prime factorization simply. Get Solution →
2. Show a factor tree example. Get Solution →
3. Name real-world uses for primes. Get Solution →
4. What does the Fundamental Theorem of Arithmetic state? Get Solution →
5. According to the text, who is credited with giving the first correct proof of the Fundamental Theorem of Arithmetic? Get Solution →
6. The prime factorization of a natural number is unique, except for what? Get Solution →
7. How is the HCF of two positive integers found using the prime factorization method? Get Solution →
8. 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.

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