GCD from Prime Decomposition/Examples/2187 and 999

Example of Use of GCD from Prime Decomposition

The greatest common divisor of $2187$ and $999$ is:

$\gcd \set {2187, 999} = 27$

$\ds 2187$

$=$

$\ds 3^7$

$\ds 999$

$=$

$\ds 3^3 \times 37$

$\ds \leadsto \ \ $

$\ds 2187$

$=$

$\ds 3^7 \times 37^0$

$\ds 999$

$=$

$\ds 3^3 \times 37^1$

$\ds \leadsto \ \ $

$\ds \gcd \set {2187, 999}$

$=$

$\ds 3^3 \times 37^0$

$\ds $

$=$

$\ds 27$

$\blacksquare$

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