Question

Prove that every composite number can be expressed as a product of prime number , and this factorization is unique except for the order in which the prime factor occur.

Answer 1

Answer:

Fundamental Theorem of Arithmetic:

Every composite number can be expressed (factorised ) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

This theorem also says that the prime factorisation of a natural number is unique, except for the order of its factors.

For example 20 can be expressed as

2×2×5

Using this theorem the LCM and HCF of the given pair of positive integers can be calculated.

Answer 2

Answer:

Every composite number can be expressed (factorised ) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. This theorem also says that the prime factorisation of a natural number is unique, except for the order of its factors.

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