NCERT

Chapter 1 Real Numbers NCERT Solutions for Class 10 Maths

📅 Published: 18 May, 2025 🔁 Updated: 18 May, 2025 🕒 Read: 2 min

1.1 Introduction

In Class 9, you learned about real numbers and irrational numbers. Now, we will study two important ideas about positive whole numbers:

  1. Euclid’s Division Algorithm:
    When you divide a number aaa by another number bbb, you get a quotient and a remainder smaller than bbb. For example, 17 divided by 5 gives quotient 3 and remainder 2.
  2. Fundamental Theorem of Arithmetic:
    Every number can be written as a unique product of prime numbers. For example, 12 = 2 × 2 × 3.

These ideas help us find the highest common factor (HCF) and understand decimals better, like when a fraction’s decimal stops or repeats.

1.2 The Fundamental Theorem of Arithmetic (Short Explanation)

Every natural number can be broken down into prime numbers multiplied together. For example,

  • 12 = 2 × 2 × 3
  • 30 = 2 × 3 × 5

The Fundamental Theorem of Arithmetic says:
Every composite number has a unique prime factorization, except for the order of the factors. This means no matter how you factor a number into primes, the list of prime factors is always the same (just the order can change).

For example,
12 = 2 × 2 × 3 is the same as 3 × 2 × 2.

This theorem helps us understand numbers better and is very important in math.

Answer:

Answer:

Answer:

Answer: