is there a formula to calculate the number of factors?

[mgaur101]

Hello Everybody,

This is my first visit to this site and i have seen one guy asked a question to find out the total no. of factors for - 3841

Solutions -

3841, first try to find out that given no. is close to which no.'s cube or square.Here 3841 is near by cube of two numbers one is 15 and another is 16.
cube of(15) is = 3375 and 16 is = 4096
4096-3841 = 255(which is also near to square of 16)
here my trick to solve the questions is that, divide the no. as much as possible.
so here i can say that -
4096 - 3841 = 256-1 or
4096-(256-1)
(16)³ - (16)² - 1 = 3841
now power of 16 will be 1 (as 3-2),so we can say that
16-1 = 15
3*5 = 15
here power of 3 and 5 is 1 so using the formula
no. of factors = (p+1)*(q+1) where p & q are the powers
2*2 = 4(ANSWER)
so here is your answer.


I do not know whether this trick will help u or not but i personally use this trick(divide as much as u can) to solve any question.


Cheers,
MANISH GAUR

[tim]

this may work some of the time, but it seems to be too specific for general use..

[amycompton]

There is no formula you just take a look at how many different combinations there are of prime factors.

So in this case

WE have 3, 7, (7 x 7 = 49), (7 x 3 = 21), (3 x 3 = 9) (9 x 7 = 63), (49 x 3 = 147) , 441, and 1

So for 441 we have total of 9 factors. Just always remember that 1 and the number it self is also a factor.

[tim]

thanks..

[nskphotography]

What David was saying in a more simplified way:

To find the total # of factors...

1) Break the # down into its prime factorization (doesn't matter what 2 factors you start with, just make a factor tree)

2) Write out the prime factorization, simplifying it into exponential form

3) Add "1" to each exponent attached to each prime

4) Multiply all the final exponents to get the total # of factors

Example:

441
49 x 9
7 x 7 x 3 x 3

Prime factorization: (7^2)(3^2)
Add "1" to the 2 sevens and add "1" to the 2 threes
To get THREE sevens and THREE twos
THREE times THREE = NINE factors total.

Tah-dah!

Hope this helps.

[tim]

thanks. let us know if there are any further questions on this one..

[Abhilash RoyG309]

One quick deduction is that, squares (like 1, 4, 9, ....) have odd number of factors.

[RonPurewal]

One quick deduction is that, squares (like 1, 4, 9, ....) have odd number of factors.

This is true, yes.