Puzzle 8-13-2008

[Wyverex]

I've yet to try these but they look more challenging!


1)  If we list all the natural numbers below 10 that are multiples of 3 
or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.


2)  The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?


3)  A Pythagorean triplet is a set of three natural numbers, a  b  c, 
for which,
a2 + b2 = c2

For example, 32 + 42 = 9 + 16 = 25 = 52.

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.