GCD from Prime Decomposition/Examples/121 and 66

Example of Use of GCD from Prime Decomposition

The greatest common divisor of $121$ and $66$ is:

$\gcd \set {121, 66} = 11$

$\ds 121$

$=$

$\ds 11^2$

$\ds 66$

$=$

$\ds 2 \times 3 \times 11$

$\ds \leadsto \ \ $

$\ds 121$

$=$

$\ds 2^0 \times 3^0 \times 11^2$

$\ds 66$

$=$

$\ds 2^1 \times 3^1 \times 11^1$

$\ds \leadsto \ \ $

$\ds \gcd \set {121, 66}$

$=$

$\ds 2^0 \times 3^0 \times 11^1$

$\ds $

$=$

$\ds 11$

$\blacksquare$

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