SOLUTION: What is the easiest way to express a number as a product of its prime numbers. Let's say 585. If I'm in a test how can i resolve this effectively? please help... Thanks

Question 179662: What is the easiest way to express a number as a product of its prime numbers. Let's say 585. If I'm in a test how can i resolve this effectively? please help...
Thanks
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
Mathematicians are interested in the prime numbers because they form the building blocks for the natural numbers in the same way that atoms form the building blocks for more complex molecules. Every natural number can be factored into a product of prime numbers, the prime numbers being the indivisible "atoms" of our number system. One of the most useful applications of large prime numbers is in the construction of secret codes. These codes are based on numbers that are the product of two very large prime numbers. The reason such codes are very difficult to break is that there is no quick method for finding the prime factors of large numbers. It is extremely unlikely that anyone will discover a fast method. Modern methods for finding prime factors are only slightly better than the method of checking all possible divisors. A thousand digit number may require hundreds of years of computing to find its prime factors. There is little work involved in the encoding and decoding of the message because both of these people know one of the prime factors. Not only is the secure transmission of information essential for national security, but it is also important for banks and large corporations.
Let me know if you come up with a quick method: we could be rich
:
585 is obviously divisible by 5. Try to use the rules of divisibility to speed up the process
:
5*117
:
now we know by rules of divisibility that 117 is divisible by 9 because the digits of the number are divisible by 9
:
so now we have 5*3*3*13.....you have all your primes

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