GCD from Prime Decomposition/Examples/51 and 87

Example of Use of GCD from Prime Decomposition

The greatest common divisor of $51$ and $87$ is:

$\gcd \set {51, 87} = 3$

$\ds 51$

$=$

$\ds 3 \times 17$

$\ds 87$

$=$

$\ds 3 \times 29$

$\ds \leadsto \ \ $

$\ds 51$

$=$

$\ds 3^1 \times 17^1 \times 29^0$

$\ds 87$

$=$

$\ds 3^1 \times 17^0 \times 29^1$

$\ds \leadsto \ \ $

$\ds \gcd \set {51, 87}$

$=$

$\ds 3^1 \times 17^0 \times 29^0$

$\ds $

$=$

$\ds 3$

$\blacksquare$

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