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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

### 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.