Exercise · ZW-FUNDAMENTAL-THEOREM-OF-ARITHMETIC-004 · ★☆☆ Basic
How many distinct prime factors does \(42\) have?
Choose one option.
Show answer
- B. 3
Explanation
\(42 = 2 \cdot 3 \cdot 7\) has three distinct primes. The option that says 1 confuses the number of factors with the number of distinct primes.
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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- ZW-FUNDAMENTAL-THEOREM-OF-ARITHMETIC-007 If n = 2^a · 3^b and n = 72, what are a and b?
- ZW-FUNDAMENTAL-THEOREM-OF-ARITHMETIC-008 What is the least common multiple of 2^3 · 5 and 2 · 3^2?
- ZW-FUNDAMENTAL-THEOREM-OF-ARITHMETIC-009 How many positive divisors does 60 = 2^2 · 3 · 5 have?
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