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Numbers: Formulas, Tricks, Examples

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  A number system relates quantities and symbols. The base or radix of a number system represents the number of digits or basic symbols in that particular number system. Decimal is a base (or radix) 10 numeral system. This means that the system has ten symbols or numerals to represent any quantity. These symbols are called Digits. The ten symbols are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. decimal number system, also called Hindu-Arabic, or Arabic, number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals. Types of Numbers R eal numbers:  Real numbers comprise the full spectrum of numbers. They can take on any form – fractions or whole numbers, decimal points or no decimal points. The full range of real numbers includes decimals that can go on forever and ever without end. For Example: 8, 6, 2 +  , 3/5 etc. N atural numbers:  A natural number is a number that comes naturally. Natural Numbers are counting numbers fr...
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LCM and HCF: Formulas, Tricks, Examples

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  Factors and Multiples:   If a number x divides another number y exactly, we say that x is a factor of y. Also y is called a multiple of x. Highest Common Factor (HCF) The H.C.F. of two or more than two numbers is the greatest number that divides each one of them exactly. There are two methods for determining H.C.F.: 1. Prime factorization method We can determine the H.C.F. of 144, 180 and 108 from following process. 144 =  2 × 2  × 2 × 2 ×  3 × 3 108 =  2 × 2  ×  3 × 3  × 3 180 =  2 × 2  ×  3 × 3  × 5 In prime factoriation of the above mentioned three numbers, the common factorization is 2 × 2 × 3 × 3 = 36. Thus, required H.C.F. of 144, 180 and 108 is 36. 2. Division Method We can determine the H.C.F. of above mentioned numbers from the following process : Thus, the H.C.F of 144 and 180 is 36. Now, we find the H.C.F of 36 and 108. So, required H.C.F is 36. Lowest Common Multiple (LCM) The L.C.M. of two or more than two n...
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