How was Aryabhata’s kuttakara method related to the Euclidean algorithm?

Aryabhata’s kuttakara method, or "pulverizer," was a sophisticated technique for solving linear indeterminate equations. Its relationship to the Euclidean algorithm is fundamental: the kuttakara process involves breaking down a mathematical problem into a series of smaller problems by iteratively reducing coefficients.1

This recursive reduction of coefficients is essentially the same procedure used in the Euclidean algorithm to find the greatest common divisor of two numbers through successive division and calculation of remainders. Furthermore, the kuttakara method is closely related to the theory of continued fractions, as the Euclidean algorithm provides the successive quotients necessary for such expansions. By employing this systematic approach, Aryabhata provided a general solution for linear indeterminate equations that remains a significant milestone in the history of Indian mathematics.21