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If the HCF of 210 and …

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If the HCF of 210 and 55 is expressible in the form 210×5+55y then find y..

Posted by Vivek Pal 6 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Devagalla Satyanarayana 6 years, 8 months ago

210=55×3+45...........(1) 55=45×1+10..............(2) 45=10×4+5................(3) 10=5×2+0 So here HCF (210,55)=5 From equation (3), 5 can be written as 5=45—10×4..........(4) Now from (2) 10=55—45×1,now this value substitute in equation (4) in place of 10 Then we get, 5=45—(55—45×1)×4 After simplifying we will get 5=45×5—55×4.......(5) Now,from (1) 45=210—55×3, this value substitute in equation (5) 5=(210—55×3)×5—55×4, after simplifying we will get 5=210×(5)+55×(-19)....Now this one compare with given equation that 5=210×5+55×x Then X=–19 is the answer

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