For some a and b ,HCF of 55 and 210 is 210a + 55b ,then find the value

1.	For some a and b ,HCF of 55 and 210 is 210a + 55b ,then find the value of a and b
Answer» Here hcf of 55 and 210 is 5 then by euclid division process _210=55×3+45_a 55=45×1+10_b45=10×4+5_c10=5×2+0_dTaking (c) steps as 5=45-10×45=45-(55-45×1)×45=45×5-55×45=(210-55×3)×5-55×45=(210×5)+{55×(-19)}Thus,a=5and b=-19 HCF of 210 & 55210 = 55× 3 + 45 ….....(i)55 = 45 × 1 +10 ….........(ii)45 = 10 ×4 +5 …...........(iii)10 = 5 ×2 + 0hence HCF of 210 & 55 = 5now from (iii), we get45 = 10 ×4 + 5so 5 = 45 – 10×45 = 45 – (55 – 45)×45 = 45 – 55×4 + 45×45 = 45 ×5 – 55×45 = (210 – 55×3) ×5 – 55×45 = 210×5 – 55×15 – 55×45 = 210×5 – 55×195 = 210 x + 55 ywhere x = 5, y = –19\xa0

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