Chapter 1
Real Numbers
In Class 10, Chapter 1 introduces real and irrational numbers. It begins with Euclid’s
Division Lemma, stating that if you have two positive numbers, a and b, you can divide
a by b and get a unique quotient q and remainder r. Euclid’s Division algorithm uses
this idea to find the Highest Common Factor (HCF) of two positive numbers. Then, the
chapter talks about the Fundamental Theorem of Arithmetic, which helps find both
the Lowest Common Multiple (LCM) and HCF of two positive numbers. Lastly, it covers
irrational and rational numbers, along with their decimal forms, using this theorem.
Topics Covered in Class 10 Maths Chapter 1 Real Numbers :
Important Steps:
The Fundamental Theorem of Arithmetic talks about how every number can be
expressed as a unique product of prime numbers. To understand this, we look at
examples and reasons. We also prove that sqrt2,3–√,sqrt2,3, and 5–√5 are
irrational.
To find the highest common factor (HCF) of two positive numbers, follow these steps:
Real Numbers
Euclid’s Division Lemma
Fundamental Theorem of Arithmetic
Irrational Numbers
Rational Numbers
1.
Use Euclid’s division method to divide the larger number by the smaller one. This
gives a quotient and a remainder.
2. If the remainder is zero, the smaller number is the HCF. If not, repeat the division
with the smaller number and the remainder.
3. Keep repeating this process until the remainder becomes zero. The divisor at this
stage will be the HCF. This works because the HCF of two numbers is the same as
the HCF of the smaller number and the remainde1:57
