Mathematics I / Primes and the Fundamental Theorem of Arithmetic
Practice question · Select all that apply

Select every statement that the Fundamental Theorem of Arithmetic guarantees.

Hints
  1. The theorem has two halves: existence of a factorization and uniqueness of it.
  2. If two integers had the same factorization, they would be the same product, hence the same number.
Show the answer
  • A. Every integer greater than 1 can be written as a product of primes
  • B. Since 60 = 2 x 2 x 3 x 5, no other collection of primes multiplies to 60
  • D. That prime factorization is unique apart from the order of the factors
Why

Existence plus uniqueness is the whole theorem, and the 60 statement is uniqueness applied. 1 is excluded because it is not greater than 1 and has no prime factors at all. And identical factorizations force identical products, so distinct integers can never share one.

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