Question 179657: Based on my previous questions and the answer provided:
``Hello I have a question regarding the easiest way to find the positive divisors of a number. I know there is a way to find them in a quick way instead of going through every number. For example I have this number 372. and even though I got the answer, it willtake me for ever to come up with 1,2,3,4,6,12,32,62,93,124,186,372. Please can you explain me how can I find the positive divisors more effectively? "
Answer: "You just have to obtain the prime factor decomposition of the number and then to combine those factors in all possible forms.
If they only ask you only by the NUMBER of divisors, that's a lot easier. It's only a problem of counting. For example:
756 = (3^3) * (2^2) * 7
Any factor you may have will be a combination (product) of these factors. You have available 3 "3"s, 2 "2"s and 1 "7", so
# of ways factor "3" may appear = 3 + 1 = 4 (3^0, 3^1, 3^2, 3^3)
# of ways factor "2" may appear = 2 + 1 = 3 (2^0, 2^1, 2^2)
# of ways factor "7" may appear = 1 + 1 = 2 (7^0, 7^1)
thus: # of ways these factors may be combined = 4*3*2 = 24
=> there are 24 factors
I HAVE ANOTHER QUESTION
I think i got a little lost. I got the last part, but how did you figure out that 756 = 3^3 *2^2 *7? Where did you get the numbers from. And also one last question, I would know that there are 24 numbers, but how would i know which ones will be the divisors?
And thanks again
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! 756=2*2*3*3*3*7
:
start with a known prime factor such as 2(since this is and even number) and then factor out all the primes.
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If you know rules of divisibility use those.The digits of this number 7+5+6=18 which is divisible by 9 so we know this number is divisible by 9.
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and just keep working it down with as big of numbers as you can.
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