Question

find the hcf of 55 and 210 and express it in the form 210 x + 55 y

Answer 1

Firstly we will find the hcf of 55 and 210 by applying Euclid's division algorithm

210>55

*210=55x3+45........(1)

*55=45x1+10.......(2)

*45=10x4+5..........(3)

*10=5x2+0..........(4)

so, HCF is 5

from equation 3 we have

5=45-(10x4)

5 = 45 – (55 – 45)*4. ( from equation 2)

5 = 45 – 55*4 + 45*4

5 = 45 *5 – 55*4

5 = (210 – 55*3) *5 – 55*4

5 = 210*5 – 55*15 – 55*4

5 = 210*5 – 55*19

5 = 210a + 55b

where a = 5, b = –19