November 20, 2009

  • This is easy? I’d rather have my teeth drilled!!!!!

    By the way, there are some divisibility rules that can help you find the numbers to divide by. There are many divisibility rules, but the simplest to use are these:

    • If the number is even, then it’s divisible by 2.
    • If the number’s digits sum to a number that’s divisible by 3, then the number itself is divisible by 3.
    • If the number ends with a 0 or a 5, then it’s divisible by 5.

    Of course, if the number is divisible twice by 2, then it’s divisible by 4; if it’s divisible by 2 and by 3, then it’s divisible by 6; and if it’s divisible twice by 3 (or if the sum of the digits is divisible by 9), then it’s divisible by 9. But since you’re finding the prime factorization, you don’t really care about these non-prime divisibility rules. There is a rule for divisibility by 7, but it’s complicated enough that it’s probably easier to just do the division on your calculator and see if it comes out even.

    If you run out of small primes and you’re not done factoring, then keep trying bigger and bigger primes (11, 13, 17, 19, 23, et ) il you find something that works — or until you reach primes whose squares are bigger than what you’re dividing into. Why? If your prime doesn’t divide in, then the only potential divisors are bigger primes. Since the square of your prime is bigger than the number, then a bigger prime must have as its remainder a smaller number than your prime. The only smaller number left, since all the smaller primes have been eliminated, is 1. So the number left must be prime, and you’re done.

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