for some a and b if hcf of 55 and 210 is 210a +55b then find the value of a and b
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the hcf of 55 and 210 is 5
by euclid method -
210 = 55 ×3 +45
55= 45 × 1 +10
45= 10 ×4+5
10= 5× 2 +0
r=0
now,
by linear combination
5 =45-10×4
5=45-(55-45×1) ×4
5= 45-55×4+45×1
5=45×2-55×4
5=(210-55×3)×2-55×4
5=210×2-55×6 -55×4
5=210×2 -55×10
so the value of a and b is 2 and -10
by euclid method -
210 = 55 ×3 +45
55= 45 × 1 +10
45= 10 ×4+5
10= 5× 2 +0
r=0
now,
by linear combination
5 =45-10×4
5=45-(55-45×1) ×4
5= 45-55×4+45×1
5=45×2-55×4
5=(210-55×3)×2-55×4
5=210×2-55×6 -55×4
5=210×2 -55×10
so the value of a and b is 2 and -10
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