Practice question · Multiple choice
1 is neither prime nor composite. Why is it excluded rather than counted as prime?
Hints
- Write 6 as a product of primes, then insert some 1s.
- What does the fundamental theorem claim is unique?
Show the answer
D. Because unique factorisation would fail, with 6 factorable many ways
Why
The exclusion protects the theorem. Admitting 1 makes every factorisation non-unique, which is exactly the property the fundamental theorem of arithmetic asserts.
Practise Primes and the Fundamental Theorem of Arithmetic
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