Real Numbers Exercise 1-2 – Unit 1 – New One with Best answers, AP Class X mathematics Exercise 1-2, Here is the complete answers of Exercise 1-2. We hope this will help you and support your preparation …. Thank you

## Real Numbers Exercise 1-2 – Unit 1 – New One with Best answers

## Real Numbers Exercise 1-2

**Real Numbers Exercise 1-2 – Unit 1 – New One with Best answers**

Theorem-1.2 : (Fundamental Theorem of Arithmetic) : Every composite number can be

expressed (factorised) as a product of primes, and this factorization is unique, apart

from the order in which the prime factors occur.

Example 3. Consider the numbers 4n

where n is a natural number. Check whether there is any

value of n for which 4n

ends with the digit zero?

Solution : For the number 4n

to end with digit zero for any natural number n, it should be

divisible by 2 and 5. This means that the prime factorisation of 4n

should contain the prime

number 5 and 2. But it is not possible because 4n

= (2)2n so 2 is the only prime in the factorisation

of 4n

. Since 5 is not present in the prime factorization, there is no natural number n for which 4n

ends with the digit zero.

You have already learnt how to find the HCF (Highest Common Factor) and LCM

(Lowest Common Multiple) of two positive integers using the Fundamental Theorem of Arithmetic

in earlier classes, without realizing it! This method is also called the prime factorization method.

Let us recall this method through the following example.

**For Real Numbers Exercise 1-1**

#### For Practice Exams check it