Express the HCF of numbers $72$ and $124$ as a linear combination of $72$ and $124$

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Solution

$124 = 72 * 1 + 52$
$⟹ 72 = 52 * 1 + 20$
$⟹ 52$ $= 20 * 2 + 12$
$⟹ 20 = 12 * 1 + 8$
$⟹ 12 = 8 * 1 + 4$
$⟹ 8 = 4 * 2$ $4 = 12 - 8 * 1 = 12 - (20 - 12) * 1 = 12 * 2 - 20$
$= (52 - 20 * 2) 2 - 20 = 52 * 2 - (72 - 52) * 5$
$= (124 - 72) * 7 - 72 * 5 = 124 * 7 - 72 * 12$
$⟹ 4 = 124 * 7 - 72 * 12$

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