Mathematics for Standard X

Chapter no. 1 Real Numbers
Today we are going to learn the most important topic from chapter 1 of your Mathematics textbook.
The Fundamental Theorem of Arithmetic :-
We know the prime numbers and composite numbers
a) Prime numbers :- The numbers which have only two factors i.e. one and the number itself. e.g  2, 3, 5, 7, 11 etc.
b) Composite numbers :- The numbers which have more than two factors are called Composite numbers. e.g 4, 6, 8, 9, 10 etc.
Now,
The Fundamental Theorem of Arithmetic:- "Every Composite number can be expressed (factorised) as a product of primes, and this factorisation is unique,  apart from the order in which the prime factors occur."
e.g  The prime factors of  Composite number  20
         20 = 2 × 2 × 5 , this prime factorisation is unique , we have change only their order i.e 20 = 5 × 2 ×2 or      20 = 2 × 5 ×2

Now , HCF ( Highest common factor) :- Product of the smallest power of each common prime factor in the numbers.

LCM ( Lowest common multiple) :- Product of the greatest power of each prime factor, involved in the numbers.

The formula of HCF and LCM of two numbers are
HCF × LCM = Product of two numbers
      Or
HCF × LCM = a × b
 ( here a and b are two given numbers)

Now  observe the  examples

The video of Fundamental Theorem of Arithmetic and Exercise 1.2 are available in following link

https://youtu.be/Jxw5e1yHPNk ( The Fundamental Theorem of Arithmetic)

https://youtu.be/czaQEKIFkyU ( Exercise 1.2 Q.2)

https://youtu.be/irrMsU0qhh8(Exercise 1.2 Q.3)

Home work - Solve Exercise 1.2 ( Q.1 to Q.4 )