Question

If
HCF(1008,20)=HCF (20, a) = HCF (a, b) ,1008=20×q+a and 20=a×m+b ,
q,a,m and b being positive integers satisfying
Euclid's division lemma what could the values of a and b?​

Answer 1

Given :  HCF(1008,20)=HCF (20, a) = HCF (a, b) ,1008=20×q+a and 20=a×m+b , q,a,m and b being positive integers satisfying

Euclid's division lemma

To find : possible values of a & b

Solution:

HCF(1008,20) = HCF (20, a) = HCF (a, b)

1008=20×q + a  

20 = a×m + b ,

HCF(1008,20)   = 4

HCF (20, a) = 4  => a = 4k  k is coprime with   5  

a can be  4  ,  8  ,  12 , 16    a < 20  

∵ 1008=20×q + a  

=>  a = 8  will satisfy  this

HCF (a, b)   = 4 => HCF ( 8 ,b)  =  4   => b = 4n  where n is coprime with 2

b  can be  4 , 12 , 20

20=a×m+b ,

=> 20  = 8 m  +  b       => b < 8

=> 20 = 8 *2  + 4

=> b = 4

a = 8   &  b = 4

values of a and b  can be  8 & 4

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