Exercise · ZW-UNIQUE-FACTORIZATION-DOMAIN-003 · ★☆☆ Basic
Using \(360=2^3\cdot3^2\cdot5\) and \(84=2^2\cdot3\cdot7\), what is the greatest common divisor of 360 and 84?
Choose one option.
Show answer
- B. 12
Explanation
Take each common prime with its smaller exponent: \(2^2\cdot3=12\). The primes 7 and 5 are not common, and 24 does not divide 84.
Review the concept: Unique factorization domain
An integral domain \(D\) in which every nonzero nonunit element \(a\) is a product of irreducibles \(p_i\), and this factorization is unique up to order and associates.
\[a=p_1p_2\cdots p_r\]
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