Every integer n≥2 factors as a product of primes, uniquely up to order.
Answer
n
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Prime factors
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Prime‑power form
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Check product
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# distinct primes
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Reason Why
(Existence) If n≥2 is composite, write n=ab with a,b≥2; repeat until primes — the process terminates. (Uniqueness) If n=p_1⋯p_r=q_1⋯q_s with primes, then by Euclid’s lemma a prime dividing a product divides one factor; match equal primes and cancel, showing the multisets are equal. Hence factorization is unique up to order.