find the HCF of 135&225 & express it in the form of 135x & 225y

Asked by apporv1999 | 27th Jul, 2014, 09:24: AM

Expert Answer:

A p p l y i n g space E u c l i d apostrophe s space d i v i s i o n space l e m m a space t o space 135 space a n d space 225 comma space w e space g e t  225 equals 135 cross times 1 plus 90...... left parenthesis i right parenthesis  S i n c e space t h e space r e m a i n d e r space 90 not equal to 0. space S o comma space w e space c o n s i d e r space d i v i s o r space 135 space a n d space r e m a i n d e r space 90 space a n d space a p p l y space d i v i s i o n space l e m m a space t o space g e t  135 equals 90 cross times 1 plus 45...... left parenthesis i i right parenthesis  S i n c e space t h e space r e m a i n d e r space 45 not equal to 0. space S o comma space w e space c o n s i d e r space d i v i s o r space 90 space a n d space r e m a i n d e r space 45 space a n d space a p p l y space d i v i s i o n space l e m m a space t o space g e t  90 equals 45 cross times 2 plus 0...... left parenthesis i i i right parenthesis  A t space t h i s space s t a g e space r e m a i n d e r space i s space z e r o. space T h e r e f o r e comma space t h e space l a s t space d i v i s o r space 45 space i s space t h e space H C F space o f space 135 space a n d space 225.  F r o m space left parenthesis i i right parenthesis comma space w e space g e t 45 equals 135 minus 90 cross times 1 rightwards double arrow 45 equals 135 minus open parentheses 225 minus 135 cross times 1 close parentheses cross times 1 space space space space space space space space space space space left parenthesis f r o m left parenthesis i right parenthesis right parenthesis rightwards double arrow 45 equals 135 minus 225 plus 135 rightwards double arrow 45 equals 135 cross times 2 plus 225 cross times left parenthesis minus 1 right parenthesis   T h e r e f o r e space 45 equals 135 x plus 225 y space w h e r e space x equals 2 space a n d space y equals minus 1

Answered by Vijaykumar Wani | 28th Jul, 2014, 10:35: AM