Yes, that will help you show that gcd(a,b,c) divides gcd(c,d). Then you have to show the converse.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?
The Greatest Common Denominator (GCD) is the largest number that can evenly divide two or more given numbers. It is also known as the Greatest Common Factor (GCF) or Highest Common Factor (HCF).
The GCD can be calculated using different methods, such as finding the prime factorization of each number and then identifying the common factors, or using the Euclidean algorithm which involves repeated division and finding the remainder until the remainder is 0.
The GCD is important in simplifying fractions, finding equivalent fractions, and solving problems involving ratios and proportions. It is also used in performing operations with fractions, such as addition, subtraction, multiplication, and division.
Yes, the GCD is always unique for a given set of numbers. This means that regardless of the method used to calculate it, the result will always be the same.
Yes, the GCD can be larger than the smallest number in a set. This can happen when the smallest number is not a factor of the other numbers in the set, but another larger number is a common factor.