The rational numbers and irrational numbers make up the set of real numbers. A number can be classified as a natural, whole, integer, rational, or irrational. The real numbers under the operations of addition and multiplication obey basic rules, known as the properties of real numbers. The type of number we usually use, such as 1, 15.82, -0.1, 3 by 4, etc. Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers. They are called "Real Numbers" because they are not Imaginary Numbers. Here we continue the discussions about real numbers starting with Eulicid's Division Lemma and The Fundamental Theorem of Arithmetic. According to the Eulicid's Division Algorithm, we find the steps to find HCF of two positive integers a and b with a is greater then b. Additionally, in The Fundamental Theorem of Arithmetic, it is also explained how Every composite number can be expressed as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur.