Find the GCD of 24 and 32 using Extended Euclidean algorithm. | Discrete Structures 2079

Discrete Structures20795 marksNumerical: extended Euclidean algorithmExtended Euclidean Algorithm

Find the GCD of 24 and 32 using Extended Euclidean algorithm. [5]

$a = 32$ , $b = 24$ (arrange larger first) - Goal: find $\gcd(24, 32)$ and Bezout coefficients $s, t$ such that $\gcd = s \cdot a + t \cdot b$ . Step Equation Quotient Remainder ------------------------------------- 1 $32 = 1 \cdot 24 + 8$ 1 8 2 $24 = 3 \cdot 8 + 0$ 3 0 The last non-zero remainde...

$a = 32$, $b = 24$ (arrange larger first) - Goal: find $\gcd(24, 32)$ and Bezout coefficients $s, t$ such that $\gcd = s \cdot a + t \cdot b$. Step Equation Quotient Remainder ------------------------------------- 1 $32 = 1 \cdot 24 + 8$ 1 8 2 $24 = 3 \cdot 8 + 0$ 3 0 The last non-zero remainde...