Exercise · ZW-GREATEST-COMMON-DIVISOR-008 · ★★☆ Intermediate
If \(d=\gcd(a,b)\) with \(a,b\) nonzero, what is \(\gcd(a/d,\,b/d)\)?
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- B. 1
Explanation
Dividing by the gcd removes every common factor: \(a/d\) and \(b/d\) are coprime. For example, \(84/42=2\) and \(126/42=3\).
Review the concept: Greatest common divisor
The greatest common divisor \(\gcd(a,b)\) of two integers \(a\) and \(b\), not both zero, is the largest integer that divides both.
\[\gcd(a,b)=\max\{d\in\mathbb{Z}:\ d\mid a,\ d\mid b\}\]
More practice problems: greatest common divisor
- ZW-GREATEST-COMMON-DIVISOR-001 Compute gcd(12,18).
- ZW-GREATEST-COMMON-DIVISOR-002 Compute gcd(35,64).
- ZW-GREATEST-COMMON-DIVISOR-003 Compute gcd(0,9).
- ZW-GREATEST-COMMON-DIVISOR-004 Compute gcd(48,180).
- ZW-GREATEST-COMMON-DIVISOR-005 Compute gcd(84,126).
- ZW-GREATEST-COMMON-DIVISOR-006 Compute gcd(1023,63), that is, gcd(2^10-1, 2^6-1).
- ZW-GREATEST-COMMON-DIVISOR-007 For which value of b does gcd(20,b)=4 hold?
- ZW-GREATEST-COMMON-DIVISOR-009 How many integers n with 1≤ n≤100 satisfy gcd(n,100)=1?
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