Question

using Euclid's division of algorithm find:

1.). If 'd' is the hcf of 12576 and 4052, then find the value of x and y satisfying "d = 4052x +12576y."

Answer 1

Hi there!

Given,
HCF (4052, 12576) = d

12576 = 3 × 4052 + 420
 
4052 =  420 × 9 + 272
   
420 =  272 × 1 + 148

272 =   148 × 1  + 124
 
148 = 124 × 1 + 24
   
124 =  5 × 24 +  4
   
24  =  6 × 4  +   0

So,
HCF = 4 (d)

4 = 124 - 5 × 24 

= 124 - 5 × (148 - 124)
   
= 6 × 124 - 5 × 148
  
= 6 × (272 - 148) - 5 × 148
 
= 6 × 272 - 11 × 148
  
= 6 × 272 - 11 × (420 - 272
   
= 17 × 272 - 11 × 420
 
= 17 × (4052 - 420 × 9) - 11 × 420
  
= 17 × 4052  -  164 * 420 
   
= 17 × 4052 - 164 × (12576 - 3 × 4052)
  
= 509 × 4052 - 164 × 12576

Hence,
x = 509 n' b = -164.

[ Thank you! for asking the question. ]
Hope it helps!