Question

Find the HCF of 135 and 620and express it as a linear combination of 135 and 620

Answer 1

I hope it will help you

Answer 2

using Euclid's division lemma
$620 = 135 \times 4 + 80 \\ 135 = 80 \times 1 + 55 \\ 80 = 55 \times 1 + 25 \\ 55 = 25 \times 2 + 5 \\ 25 = 5 \times 5 + 0$
so HCF(135,620)=5
For representing this with linear combination,start from second last equation
$5 = 55 - 25 \times 2 \\ 5 = 55 - (80 - 55) \times 2 \\ 5 = 135 - 80 - \\ (620 - 135 \times 4 - 135 + 80) \times 2 \\ = 135 - 620 + 135 \times 4 \\ -2(620 - 135 \times 4)+ 2 \times \\ 135 - 2(620 - 135 \times 4) \times 2 \\ 5 = (23 ) 135 - (5) 620$