Introduction

☼ Factors & Multiples : If   ‘a’   divides  ‘b’  exactly, then we say that  ‘a’  is a factor of  ‘b’  and  we write,  a | b.  In this case,  ‘b’  is called  a  multiple of   ‘a’.

☼ An  Important  Result   :   If   ‘p’   is    prime    and   ‘a’,   ‘b’  are  any  integers,   then  p | ab    p | a   or   p | b    (or   p | a   &   p | b ).

 e.g. 3 | 60    3 | 6   but   3  † 10.

☼ Highest Common Factor (H.C.F.  or  G.C.D.  or  G.C.M.) : The H.C.F. of  two or more than two numbers is the greatest number that divides each one of  them exactly. This is also known as greatest common divisor ( G.C.D.)  or  greatest  common  measure ( G.C.M.).

The  H. C. F.  of   a  and  b  is denoted by  (a, b).    [  i.e.  ( 15, 21)  =  3    ]

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