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We say that an integer c is a common divisor of integers a and b if cla and clb. We say c is the greatest common divisor if c is the largest common divisor of a and b, and in this case we denoted c by gcd(a, b). For example, the common divisors of a = 30 and b = 18 are 1, 2, 3, and 6. As 6 is the largest of these divisors, gcd(30, 18) = 6. (a) Compute the greatest common divisor of 63 and 255. (We'll later see an efficient way to do this, but for now try to do this "by hand.") (b) Show if c is a common divisor of a and b, then c is also a common divisor of ax and bx for every integer x.

We say that an integer c is a common divisor of integers a and b if cla and clb. We say c is the greatest common divisor if c is the largest common divisor of a and b, and in this case we denoted c by gcd(a, b). For example, the common divisors of a = 30 and b = 18 are 1, 2, 3, and 6. As 6 is the largest of these divisors, gcd(30, 18) = 6. (a) Compute the greatest common divisor of 63 and 255. (We'll later see an efficient way to do this, but for now try to do this "by hand.") (b) Show if c is a common divisor of a and b, then c is also a common divisor of ax and bx for every integer x.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3. We say that an integer c is a common divisor of integers a and b if cla and c|b. We say c is the greatest common divisor if c is the largest common divisor of a and b, and in this case we denoted c by gcd(a, b). For example, the common divisors of a = = 30 and b = 18 are 1, 2, 3, and 6. As 6 is the largest of these divisors, gcd(30, 18) = 6. (a) Compute the greatest common divisor of 63 and 255. (We'll later see an efficient way to do this, but for now try to do this "by hand.") (b) Show if c is a common divisor of a and b, then c is also a common divisor of ax and bx for every integer x.
Transcribed Image Text:3. We say that an integer c is a common divisor of integers a and b if cla and c|b. We say c is the greatest common divisor if c is the largest common divisor of a and b, and in this case we denoted c by gcd(a, b). For example, the common divisors of a = = 30 and b = 18 are 1, 2, 3, and 6. As 6 is the largest of these divisors, gcd(30, 18) = 6. (a) Compute the greatest common divisor of 63 and 255. (We'll later see an efficient way to do this, but for now try to do this "by hand.") (b) Show if c is a common divisor of a and b, then c is also a common divisor of ax and bx for every integer x.
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