Question

if the HCF of 420 and 130 is expressible in the form of 420 P + 130 Q then the value of P + Q is

Answer 1

$\textbf{Given:}$

$HCF(420,130)=420\,P+130\,Q$

$\textbf{To find:}$

$\text{The value of P+Q }$

$\textbf{Solution:}$

$\text{By division algorithm, we get}$

$420=(3{\times}130)+30$.......(1)

$130=(4{\times}30)+10$........(2)

$30=(3{\times}10)+0$.........(3)

$\therefore\textbf{H.C.F(420,130)=10}$

$\text{Now,}$

$\text{From (2), we can write}$

$10=130-(4{\times}30)$

$10=130-(4(420-3{\times}130))$

$10=130-4(420)+12{\times}130$

$10=-4(420)+13{\times}130$

$\text{Comparing with 420\,P+130\,Q we get}$

$P=-4\;\;\text{and}\;\;Q=13$

$P+Q=-4+13=9$

$\textbf{Answer:}$

$\textbf{The value of \bf\,P+Q is 9}$