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PRPPERTIES OF GCF:

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by pemdas » Mon Oct 29, 2012 1:01 pm
let's elaborate

to prove something in the number theory we have to narrow an objective: real numbers, primes and non-primes, their GCF (greatest common factor)

primes: 2 and 3, the difference of one from another will be 1. This an example of primes following each other. All primes have GCF equal to 1, hence the primes' difference >= (greater or equal than) 1 always.

non-primes: one number may contain itself as a factor twice, 2 and 4. CGF is 2, as per rule GCF is obtained from sorting out each number's prime factors and then joining them to get each number's prime factor included exactly as many times as it's found in the prime factorization of the numbers for which GCF is sought. 4-2=2 (difference) will always be >= 1
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