Question

Find the HCF of 55 and 210. Express it as a linear combination of 55 and 210, ie. HCF of 55 and 210 = 210a + 55b, for some a and b.

Answer 1

Answer:

A=5, B= -19

Step-by-step explanation:

HCF of 210 and 55

255= 55×3+45 --------- 1

55=45×1+10 -------- 2

45=10×4+5 ---------- 3

10=5×2+0.

From prime factorization:

HCF of 210 and 55 =5  

Putting value from equation 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