Exercise · ZW-FUNDAMENTAL-THEOREM-OF-ARITHMETIC-001 · ★☆☆ Basic
What is the prime factorization of \(12\)?
Choose one option.
Show answer
- A. \(2^2 \cdot 3\)
Explanation
\(12 = 2 \cdot 2 \cdot 3\), and its prime factors are 2 and 3. The option with \(2 \cdot 6\) includes the composite 6, which is not prime.
Review the concept: Fundamental theorem of arithmetic
Every integer greater than 1 can be written uniquely as a product of primes, up to the order of the factors. It is the foundation of most of elementary number theory.
\[n = p_1^{a_1} p_2^{a_2} \cdots p_k^{a_k}\]
More practice problems: fundamental theorem of arithmetic
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