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 Skyscrapers are tall buildings that tower in the air. The foundations of a skyscraper are laid by drilling holes in the ground and filling them with concrete. If the ground is firm, the foundations are wide so that they will spread the weight of the building and they do not go very deep. If the ground is not very firm, deep shafts of concrete are driven into the ground to anchor the skyscraper firmly.   Then a frame of steel griders or concrete beams is erected, often with a pillar like concrete core containing lift shafts and stairs. The frame and core take all the weight of the building so that the walls do not have to support the floors above. The tallest skyscraper of the world is the - Sears Tower of Chicago state (Illinois) with 110 storeys rising 443 meter. The other famous skyscraper is National Westminster Tower of Great Britain. Tallest skyscraper of the world, The Sears Chicago state.

 In class IX, you began your exploration of the world of real numbers and encountered irrational numbers.we continue our discussion on real numbers in this chapter.we begin with our two very important properties of positive integers in section 1.2 and 1. 3 ,namely the Euclid's division algorithm and the fundamental theorem of arithmetic Theorem 1.1:   According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers   q   and   r   which satisfies the condition   a = bq + r   where 0  ≤ r < b . The basis of the Euclidean division algorithm is Euclid’s division lemma. To calculate the Highest Common Factor (HCF) of two positive integers  a  and  b  we  use  Euclid’s division algorithm . HCF is the largest number which exactly divides two or more positive integers. That means, on dividing both the integers  a  and  b  the remainder is zero.