Fundamental Theorem of Arithmetic

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math

Is Euclid's theory relating to the decomposition of a composite number into the product of a finite series of primes. It states that every integer greater than 1 can be represented uniquely as a product of the prime numbers up to the order of the factors.

Every possible number has one, and only one, prime factorisation.

For example 1200 has prime-factors (factors that are prime) of 2, 3, and 5. The unique prime factorisation of 1200 is \( 2^4 \times 3 \times 5^2 \).

This theorem is the reason \( 1 \) is not a prime number, for if it was no prime factorisation would ever be unique. You could always just multiply by another 1.