November 20, 2009
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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.
Comments (8)
Makes perfect sense.
@mksmak - Maybe to you but not to me. This polynomial stuff is too hard for my little ol’ brain to comprehend.
Beer time.
No doubt about it.
@Bricker59 - I always knew we were kindred spirits! This math stuff may turn me to the hard stuff though.
I love math (once I understood it) but that would drive me to drink or eat vast amount of choclates.
@ugotafriend - I actually start school on 7 Dec. but I have been doing pre-Algebra online because I am such a math failure that I need to brush up before I start my course. I am having a hard time with the pre course so I wonder if I am going to be able to pass the actual course.
I was done halfway through your post, ha ha.
I’m a lousy at math. Surprisingly, my daughter excels in math and teaches it at the high school level. She must have inherited her math ability from my dad, who is brilliant.
@Amythist_Malaise - I have been practicing desperately so that I will at least be able to pass my course. Why should math keep me from getting my English degree I don’t know but there you have it. The irony is that my husband has his bachelors in Physics.