Question

D. Write the statement of fundamental theorem of Arithmetic.
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Answer 1

Answer:

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes (Hardy and Wright 1979, pp. 2-3). This theorem is also called the unique factorization theorem.

Answer 2

"Every composite number can be factorized as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur."

Step 1 - Existence of Prime Factorization

Existence of Prime FactorizationWe will prove this using Mathematical Induction.

Step 2 - Uniqueness of Prime Factorization