How Do You Compute the GCD of Three Numbers Using Pairwise GCD?

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SUMMARY

To compute the greatest common divisor (GCD) of three numbers a, b, and c using pairwise GCD, first calculate the GCD of a and b, denoted as d. The relationship established is that GCD(a, b, c) equals GCD(d, c). This method leverages the property that GCD(a, b, c) divides both d and c, allowing for a simplified calculation.

PREREQUISITES
  • Understanding of GCD and its properties
  • Familiarity with pairwise operations in mathematics
  • Basic knowledge of number theory
  • Ability to manipulate mathematical equations
NEXT STEPS
  • Study the Euclidean algorithm for efficient GCD computation
  • Explore the properties of divisibility in number theory
  • Learn about the application of GCD in simplifying fractions
  • Investigate algorithms for computing GCD of multiple numbers
USEFUL FOR

Students in mathematics, educators teaching number theory, and anyone interested in computational methods for finding GCDs.

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Homework Statement


Show that in order to find common denominator of a,b,c, you can first find the gcd to a and b called d.
Then gcd(a,b,c)= gcd(d,c)

Homework Equations



The Attempt at a Solution



I know that we atleast must have that gcd(a,b,c) divides d, can I use that?
 
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bobby2k said:

Homework Statement


Show that in order to find common denominator of a,b,c, you can first find the gcd to a and b called d.
Then gcd(a,b,c)= gcd(d,c)

Homework Equations



The Attempt at a Solution



I know that we atleast must have that gcd(a,b,c) divides d, can I use that?
Yes, that will help you show that gcd(a,b,c) divides gcd(c,d). Then you have to show the converse.
 

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