Real Numbers are an important topic in Class 10 Maths actually for all the classes. This chapter helps students understand numbers, “What is the prime numbers, factors, HCF, LCM, and decimal forms?”. These concepts are also useful in many other Maths chapters.
With simple explanations, examples and regular practice, Class 10 Maths Real Numbers can become easy to learn, revise and understand.
What Are Real Numbers?
Real numbers is the combination of rational numbers and irrational numbers and are represented with symbols R. These number can be represent on number line easily.
Examples of rational numbers are:
- 3
- 8/3
- 0.75
- −10
Examples of irrational numbers include:
- √2
- √3
- √5
- √7
Fundamental Theorem of Arithmetic
The Fundamental Theorem of Arithmetic says that every composite number can be expressed as a product of prime numbers in a unique way, order doesn’t matter.
For example:
60 = 2 × 2 × 3 × 5
or
60 = 2² × 3 × 5
This prime factorization is useful when finding the HCF and LCM of numbers.
HCF and LCM Example
Let us find the HCF of 24 and 36.
Prime factors:
24 = 2³ × 3
36 = 2² × 3²
For HCF, take the common factors with the smallest powers:
HCF = 2² × 3 = 12
So, the HCF of 24 and 36 is 12.
For LCM, we take all factors with the greatest powers:
LCM = 2³ × 3² = 72
Therefore, the LCM is 72.
Euclid’s Division Algorithm
Euclid’s division algorithm helps us to find the HCF of two numbers.
General form of Euclid’s Division Algorithm (a=bq+r, where r is remainder, q is quotient, b is dividend and a is dividend, 0<=r<b)
For example, to find the HCF of 135 and 225:
225 = 135 × 1 + 90
135 = 90 × 1 + 45
90 = 45 × 2 + 0
The last non-zero remainder is 45.
Therefore:
HCF = 45
This method becomes easier when you practise it step by step.
Tips to Prepare Real Numbers
To improve your Class 10 Maths preparation:
- Learn the basic definitions.
- Practise prime factorisation.
- Understand HCF and LCM methods.
- Solve Euclid’s division questions.
- Revise important examples regularly.
- Check every calculation carefully.
FAQs
What are real numbers?
Real numbers include rational and irrational numbers.
What is HCF?
HCF is the highest common factor of two or more numbers.
What is LCM?
LCM is the smallest common multiple of two or more numbers.
Why is prime factorisation important?
It helps us find HCF and LCM and understand the factors of numbers.
How can I improve in Real Numbers?
Understand the basic rules and practise different types of questions regularly.
Conclusion
Class 10 Maths Real Numbers becomes easier when you learn the concepts step by step. Practise HCF, LCM, prime factorisation, and Euclid’s division algorithm regularly. With clear concepts and daily practice, you can build confidence and prepare better for your Maths exam.