Question

if d is HCF of 40 and 65 ,find the value of integer x and y which satisfy d= 40 x +65y

Answer 1

First we will find the hcf. Since 65>45 Therefore, 64=40×1+25 40=25×1+15 25=15×1+10 15=10×1+5 10=5×2+0 Since remainder is 0 Therefore hcf is 5 To do it in linear combination we have 5=15-(10×1) 5=15-(25-15×1) 5=40-25×1-(25-40×1-25)... And so on till we get 5=40(5)+65(-3) Now comparing 40x+65y with our ans we get that , x=5 and y=-3