Question

Find the of HCF of 55 and 210. Express it as a linear combination of 55 and 210, i.e 210a+55b, for some a and b .?

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

Answer 2

• HCF of 210 and 55

255= 55×3+45 equa 1

55=45×1+10 equa 2

45=10×4+5 equa 3

10=5×2+0.

• From prime factorization:

HCF of 210 and 55 =5  

• Putting value from equa 2 and 3

45-(55-45)*4 =5  

45-55*4+45*4=5

(210-55*3)5-55*4=5  

210*5-55*15-55*4=5

5=210*5*55*19=210A+55B

From the above equation we get

• A=5

• B= -19