Question

what is fundamental theore of arithmetic

Answer 1

fundamental theory of arithmetic also called the unique factorization theorem and unique factori ration theorem states that every integer greater than 1 either is crime itself or is the product of prime numbers and that this product is unique up to the order of the factors

Answer 2

Fundamental Theorem of Arithmetic :-

Every composite number can be expressed as the product of primes , and this factorization is unique , apart from the order in which they occur.

I will explain this is in simple way.

First of all lets see what prime numbers are :

Prime Numbers are the numbers which have only 2 factors : 1 and the number itself
For example : 2 , 3 , 5 , 7 etc....

Also , lets take a look what are Composite Numbers :
 Composite Numbers are those numbers which has more than 2 factors

Example : 4 , 6 , 8 , 10 etc .....

SO, according to 

fundamental theorem of arithmetic ;

a composite number , say 120 , an be expressed as :

2 × 2 × 2 × 3 × 5 = 120

Where 2 , 3 and 5 are prime numbers.

This prime factorisation is unique , which cannot be replaced by any other prime number.

However the order can be changed :

120 = 2 × 3 × 2 × 5 × 2

Hope this helps u