Question

State the fundamental Theorem of Arithmetic​

Answer 1

Fundamental Theorem of Arithmetic

• According to this theorem, every natural number greater than 1 is either prime or can be expressed in the form of the product of its prime factors. It is also termed as the unique factorization theorem.
• For the initial series:

       2 - prime number; 3 - prime number; 4 = 2 x 2; 5 - prime number;

       6 = 2 x 3 and so on.

• It should be noted that prime numbers are ones that are divisible by 1 and the number itself. For instance, 11 can be divided only by 1 and 11, i.e. 11 = 1 x 11

Answer 2

FUNDAMENTAL THEOREM OF ARITHMETIC :  

According to the fundamental theorem of arithmetic every composite number can be written or  factorized as the product of primes and this factorization is unique, apart from the order in which the prime factors occur.  

Fundamental theorem of arithmetic , is also called, UNIQUE FACTORIZATION THEOREM.

Composite number =  product of prime numbers

Or  

Any integer greater than one, either be a prime number or can be written as a product of prime factors.

for e.g : 98 = 2 × 7 × 7 = 2 × 7²

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