1.Euclid's division lemma

2.Arithmetic Fundamental Theorem

1.14  the Fundamental theorem of arithmetic :

heorem (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 occurs.
    The prime factorisation of a natural number is unique except the order of its factors.

3.Irrational and Rational Numbers

1.3    Irrational Numbers :
  

Some Properties of irrational numbers :
(a)    The –ve of an irrational number is an irrational number.
(b)    The sum of a rational and an irrational number is an irrational number.
(c)    The product of a non–zero rational number with an irrational number is always an irrational number.
 

decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals