Question

Fundamental theorem of arithmetic states that every number x can be expressed a product of primes and this factorization is unique, apart from the order in which the prime factors occur. here the number x can be

(a) positive integer
(b) natural number
(c) composite number
(d) square number

Answer 1

The prime factors occur. here the number x can be a positive integer. Option A

Any positive integer larger than 1 can be uniquely represented as a product of prime numbers, according to the Fundamental Theorem of Arithmetic. Everything in this factorization is unique, save for the primes' order of occurrence. Negative integers and natural numbers smaller than two are not covered by the theorem.

It provides a critical understanding of the underlying principles of number theory by highlighting the central role of prime numbers in arithmetic and clarifying the special breakdown of integers into their prime factors.