GCD from Prime Decomposition/Examples/169 and 273

Example of Use of GCD from Prime Decomposition

The greatest common divisor of $169$ and $273$ is:

$\gcd \set {169, 273} = 13$

$\ds 169$

$=$

$\ds 13^2$

$\ds 273$

$=$

$\ds 3 \times 7 \times 13$

$\ds \leadsto \ \ $

$\ds 169$

$=$

$\ds 3^0 \times 7^0 \times 13^2$

$\ds 273$

$=$

$\ds 3^1 \times 7^1 \times 13^1$

$\ds \leadsto \ \ $

$\ds \gcd \set {169, 273}$

$=$

$\ds 3^0 \times 7^0 \times 13^1$

$\ds $

$=$

$\ds 13$

$\blacksquare$

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