Question

HCF of 210 and 55 is expressible in the form of 210 Into X + 55 into Y then find the value of x + Y​

Answer 1

210 = 55 * 3 + 45
55 = 45 * 1 + 10
45 = 10 * 4 + 5
10 = 5 * 2

hence 5 is the HCF.

    5 =  45  - 10 * 4          substitute the values of 10 and 45 from above equations.
       = 210 - 55 * 3 - (55 - 45 ) 4
       =  210 - 55 * 3 - 55 * 4 + 45 * 4
       =  210 - 55 * 7 + (210 - 55 * 3) * 4
       = 210 * 5 - 55 * 19

so  x = 5 and  y = -19
and x +y = 5 -19 = -14