Re: factorization

On 17 May 2007 05:28:40 -0700, Mirror <andxfiles@xxxxxxxxx> wrote:
I have made an observation about prime numbers.

All prime numbers - except 2 and 5 - have as their last digit, either
1 or 3 or 7 or 9. ( it can't be 5 because it would then be divisable
by 5 ).

We notice that the last digit of the multiplication of two prime
numbers is also 1,3,7 or 9. How is that ?

A positive integer ends in 1, 3, 7, or 9 if and only if it is not
divisible by 2 or 5. You observe that if neither of two numbers
is divisible by 2 or 5, then their product is also not divisible
by 2 or 5. This can be seen as a consequence of the "Fundamental
Theorem of Arithmetic" (see Wikipedia), which states that every
integer > 1 has a unique prime factorization, thereby prohibiting
the appearance or disappearance of factors of 2 or 5 when
integers are multiplied together.


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