use euclid's division algorithm, find which of the following numbers are co prime? and explain how?
 
                   (a)15  ,  98        
 
                   (b) 198  ,  429
 
                   (c) 837   , 2160

Asked by anshika adlakha | 27th May, 2014, 02:27: PM

Expert Answer:

left parenthesis a right parenthesis space U sin g space e u c l i d apostrophe s space d i v i s i o n space a l g o r i t h m comma space w e space h a v e 98 equals 6 cross times 15 plus 8 15 equals 1 cross times 8 plus 7 8 equals 1 cross times 7 plus 1 7 equals 7 cross times 1 plus 0 S i n c e space 1 space i s space t h e space H C F space o f space 15 space a n d space 98 comma space 15 space a n d space 98 space a r e space c o p i r m e space n u m b e r s.  left parenthesis b right parenthesis space U sin g space e u c l i d apostrophe s space d i v i s i o n space a l g o r i t h m comma space w e space h a v e 429 equals 2 cross times 198 plus 33 198 equals 6 cross times 33 plus 0 H e r e comma space 6 space i s space t h e space H C F space o f space 429 space a n d space 198 space a n d space h e n c e space t h e y space a r e space n o t space c o p r i m e space n u m b e r s  left parenthesis c right parenthesis space U sin g space e u c l i d apostrophe s space d i v i s i o n space a l g o r i t h m comma space w e space h a v e 2160 equals 2 cross times 837 plus 486 837 equals 1 cross times 486 plus 351 486 equals 1 cross times 351 plus 135 351 equals 2 cross times 135 plus 81 135 equals 1 cross times 81 plus 54 81 equals 1 cross times 54 plus 27 254 equals 2 cross times 27 plus 0 H e r e comma v 2 space i s space t h e space H C F space o f space 2160 space a n d space 837 space a n d space h e n c e space t h e y space a r e space n o t space c o p r i m e space n u m b e r s. T h u s comma space o p t i o n space left parenthesis a right parenthesis space i s space t h e space c o r r e c t space a n s w e r.

Answered by Vimala Ramamurthy | 28th May, 2014, 09:27: AM