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H.C.F. AND L.C.M. OF NUMBERS I.   Factors and Multiples :  If a number a divides another number b exactly, we say that a is 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.) or Greatest Common Divisor (G.C.D.):   The H.C.F. of two or more than two numbers is the 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 product of 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 the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is the required H.C.F.  

1.   NUMBERS      IMPORTANT FACTS AND FORMULAE I. Numeral        In Hindu & Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number.          A group of digits, denoting a number is called a numeral.         We represent a number, say 689745132 as shown below : Ten Crores (10 8 ) Crores (10 7 ) Ten Lacs (Millions) (10 6 ) Lacs (10 5 ) Ten Thousands (10 4 ) Thousands (10 3 ) Hundreds (10 2 ) Tens (10 1 ) Units (10 0 ) 6 8 9 7 4 5 1 3 2       We read it as : 'Sixty-eight crores, ninety-seven lacs, forty-five thousand, one hundred and thirty-two'.  II. Place Value or Local Value of a Digit in a Numeral In the above numeral : Place value of 2 is (2 x 1) = 2; Place value of 3 is (3 x 10) = 30; Place value of 1 is (1 x 100) = 100 and so on.