Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 abbr. greatest common divisor
from Wiktionary, Creative Commons Attribution/ShareAlike License
 Initialism of greatest common divisor.
Etymologies
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Examples

(We are looking for approximations that are good relative to the amount of space that it takes to write the rational: call gcd (a, q) = 1) a good approximation to, where c is large.)

If their gcd is not 1, then even using integers you can't reach all natural numbers, so we must have gcd=1.

All numbers beyond a certain point can be written as a *SUM* of the n's if and only if their gcd is one.

So all numbers beyond a certain point can be written as a sum of the n's if and only if their gcd is one.

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Proof: Suppose that d = gcd (a, b) and e = gcd (a  b, b) then dIa, dIb and eI (a  b) and eIb.
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