Question

Express gcd of 48 and 18 as linear combination

Answer 1

I think 6 is the linear combination
48÷18=2 remainder=12
18÷12=1 remainder=6
18÷6=3 remainder=0
so it is 6
I hope it's helpful

Answer 2

a = bq + r

$\bf\huge 48 = 18\times 2 + 12$

$\bf\huge 18 = 12\times 1 + 6$

$\bf\huge 12 = 6\times 2 + 0$

HCF (18 , 48) = 6

$\bf\huge 6 = 18 - 12\times 1$

$\bf\huge 6 = 18 - (48 - 18\times 2$

$\bf\huge 6 = 18 - 48\times 1 + 18\times 2$

$\bf\huge 6 = 18\times 3 + 48\times 1$

$\bf\huge 6 = 18\times 3 + 48\times (-1)$

$\bf\huge 6 = 18x + 48y$

Here x = 3 and y = -1

$\bf\huge 6 = 18\times 3 + 48\times (-1)$

$\bf\huge 6 = 18\times 3 + 48\times (-1) + 18\times 48 - 18\times 48$

$\bf\huge 6 = 18 (3 + 48) + 48(-1 - 18)$

$\bf\huge 6 = 18\times 51 + 48\times (-19)$

$\bf\huge 6 = 18x + 48y$

Here we have x = 51 and y = -19

Therefore x and y are not unique