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

Posted by Vini Negi 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Sudhanshu Yadav 6 years, 10 months ago

Here hcf of 55 and 210 is 5 then by euclid division process _210=55×3+45_a 55=45×1+10_b 45=10×4+5_c 10=5×2+0_d Taking (c) steps as 5=45-10×4 5=45-(55-45×1)×4 5=45×5-55×4 5=(210-55×3)×5-55×4 5=(210×5)+{55×(-19)} Thus,a=5and b=-19

1Thank You

Yogita Ingle 6 years, 10 months ago

HCF of 210 & 55
210 = 55× 3 + 45 ….....(i)
55 = 45 × 1 +10 ….........(ii)
45 = 10 ×4 +5 …...........(iii)
10 = 5 ×2 + 0
hence HCF of 210 & 55 = 5
now from (iii), we get
45 = 10 ×4 + 5
so 5 = 45 – 10×4
5 = 45 – (55 – 45)×4
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 = 210 x + 55 y
where x = 5, y = –19

3Thank You

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