Quantitative Aptitude-RS Agarwal

Apr 7th, 2015
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National Institute of Technology
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Best prescribed book for many competitive exams,includes varieties of shortcuts for distance ,speed ,time, ratios, proportions,clocks,calendars,allegations, permutations and combinations, probability and lot more...

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2. H.C.F. AND L.C.M. OF NUMBERSIMPORTANT FACTS AND FORMULAEI. Factors and Multiples : If a number a divides another number b exactly, we say that ais a factor of b. In this case, b is called a multiple of a.II. Highest Common Factor (H.C.F.) or Greatest Common Measure (G.C.M.) orGreatest Common Divisor (G.C.D.): The H.C.F. of two or more than two numbers isthe greatest number that divides each of them exactly.There are two methods of finding the H.C.F. of a given set of numbers :1. Factorization Method : Express each one of the given numbers as the productof prime factors.The product of least powers of common prime factors gives H.C.F.2. Division Method: Suppose we have to find the H.C.F. of two given numbers.Divide the larger number by the smaller one. Now, divide the divisor by theremainder. Repeat the process of dividing the preceding number by the remainderlast obtained till zero is obtained as remainder. The last divisor is the requiredH.C.F.Finding the H.C.F. of more than two numbers : Suppose we have to find theH.C.F. of three numbers. Then, H.C.F. of [(H.C.F. of any two) and (the thirdnumber)] gives the H.C.F. of three given numbers.Similarly, the H.C.F. of more than three numbers may be obtained.III. Least Common Multiple (L.C.M.) : The least number which is exactly divisible byeach one of the given numbers is called their L.C.M.1. Factorization Method of Finding L.C.M.: Resolve each one of the givennumbers into a product of prime factors. Then,

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