State fundamental theorem of arithmetic.?

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The Fundamental Theorem of Arithmetic says that any positive integer greater than 1 can be written as a product of finitely many primes uniquely up to their order. The term 'up to thier order' means that we consider 12=2×2×3 to be equivalent as 12=3×2×2. Note that a product can consist of just one prime.

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Fundamental Theorem states that 'Every composite numbers can be expressed as a product of primes and this factorisation is unique, apart from the order in which the prime factor occur'.

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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.

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The fundamental theorem of arithmetic (FTA), also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 11 either is prime itself or is the product of a unique combination of prime no.

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The fundamental theorem of arithmetic (FTA), also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 11 either is prime itself or is the product of a unique combination of prime numbers.

Answer

Answer

The Fundamental Theorem of Arithmetic
The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be uniquely factored into a product of prime numbers. In other words, any composite number can be expressed as a unique product of prime numbers.

Key Points:
- Every integer greater than 1 can be written as a unique product of prime numbers.
- Prime factorization is the process of breaking down a number into its prime factors.
- Prime numbers are numbers that have exactly two distinct factors: 1 and the number itself.
- Composite numbers are numbers that have more than two factors.

Explanation:
The Fundamental Theorem of Arithmetic is a crucial concept in number theory. It tells us that every composite number can be expressed as a unique product of prime numbers. For example, the number 12 can be factored as 2 x 2 x 3, where 2 and 3 are prime numbers.
This theorem is important because it helps us understand the structure of numbers and their relationships with prime numbers. It also allows us to efficiently find the prime factorization of any composite number, which is useful in various mathematical calculations and proofs.
Overall, the Fundamental Theorem of Arithmetic is a fundamental concept in mathematics that helps us understand the building blocks of numbers and their unique factorization properties.

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