GCD from Prime Decomposition/Examples/64 and 81

Example of Use of GCD from Prime Decomposition

The greatest common divisor of $64$ and $81$ is:

$\gcd \set {64, 81} = 1$

$\ds 64$

$=$

$\ds 2^6$

$\ds 81$

$=$

$\ds 3^4$

$\ds \leadsto \ \ $

$\ds 64$

$=$

$\ds 2^6 \times 3^0$

$\ds 81$

$=$

$\ds 2^0 \times 3^4$

$\ds \leadsto \ \ $

$\ds \gcd \set {64, 81}$

$=$

$\ds 2^0 \times 3^0$

$\ds $

$=$

$\ds 1$

$\blacksquare$

1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-4}$ The Fundamental Theorem of Arithmetic: Exercise $6 \ \text{(e)}$