Question about problem involving gcd

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In summary, GCD (Greatest Common Divisor) is the largest positive integer that divides into two given numbers without any remainder. It is calculated using the Euclidean algorithm. Gcd is always a positive integer and is used in various mathematical problems, such as simplifying fractions, finding the lowest common multiple, and solving linear equations. The main difference between gcd and lcm (Least Common Multiple) is that gcd is the largest divisor while lcm is the smallest multiple. Gcd can also be greater than the smaller of the two given numbers if the smaller number is a multiple of the larger number.
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issacnewton
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HelloI am studying the problem given in the attachement. In the solution given, it says "Similarly \( d|\gcd(a,-b) \) ". I could not understand why this is so.thanks
 

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IssacNewton said:
HelloI am studying the problem given in the attachement. In the solution given, it says "Similarly \( d|\gcd(a,-b) \) ". I could not understand why this is so.thanks
$d|\gcd(a,-b)$ follows from the fact that $d=\gcd(a,b)$.
 
  • #3
thanks...I should have realized that...
 

Related to Question about problem involving gcd

1. What is gcd and how is it calculated?

GCD (Greatest Common Divisor) is the largest positive integer that divides into two given numbers without any remainder. It is calculated using the Euclidean algorithm.

2. Can gcd be negative?

No, gcd is always a positive integer.

3. How is gcd used in solving mathematical problems?

Gcd is used in various mathematical problems, such as simplifying fractions, finding the lowest common multiple, and solving linear equations.

4. What is the difference between gcd and lcm?

GCD (Greatest Common Divisor) is the largest positive integer that divides into two given numbers without any remainder, while LCM (Least Common Multiple) is the smallest positive integer that is a multiple of two or more given numbers.

5. Can gcd be greater than the smaller of the two given numbers?

Yes, gcd can be greater than the smaller number if the smaller number is a multiple of the larger number.

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