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 Description  
 Fundamental Theorem of Arithmetic:  Every integer, N > 1, is either prime or can be uniquely written as a product of primes.
This is also known as the Unique Factorization Theorem. It essentially states that for all postive numbers larger than 1, its factorization is unique.

For Example

51 = 3*17
130 = 2*5*13
550 = 2*5^2*11
5032 = 2^3*17*37

Knowing numbers prime factorizations is unique can help in calculating the Greatest Common Divisor and Least Common Multiple of two numbers. For example, take the numbers 130 and 550; their unique factorizations are:

130 = 2*5*13
550 = 2*5*5*11

To find their GCD, you need to look at their prime factorizations and multiple which ever primes appear in both.
GCD(130,550) = 2*5 = 10

To find their LCM, multiple every factor that they both have:
LCM(130,550) = 2*5*5*11*13 = 7150