State the fundamental theorem of Arithmetic?
Answers
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. ... This theorem is also called the unique factorization theorem.
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Answer:
The statement of Fundamental Theorem Of Arithmetic is:
"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."
For example, let us find the prime factorization of 240
From the above figure,
240=2×2×2×2×3×5
=2^4×3×5
Our theorem further tells us that this factorization must be unique.
That is, there is no other way to express 240 as a product of primes.
Of course, we can change the order in which the prime factors occur.
For example, the prime factorization can be written as:
240=3×2^4×5
=2^2×2^2×3×5etc.
But the set of prime factors (and the number of times each factor occurs) is unique.
That is, 240can have only one possible prime factorization, with four factors of 2, one factor of 3,and one factor of 5
Step-by-step explanation:
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