FORMULA for DIVISORS

Hi, ans welcome to the forum

The following UDF would be one way

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Enter

Formula:

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where A1 contains your number

What version of excel are you using?

This requires Excel 2007 or later.

Data Range

	A	B	C	D	E	F	G	H	I	J	K
1	Number	Divisors
2	27	1	3	9	27
3	82	1	2	41	82
4	13	1	13
5	100	1	2	4	5	10	20	25	50	100
6	------	------	------	------	------	------	------	------	------	------	------

This array formula** entered in B2:

=IFERROR(SMALL(IF(MOD($A2,ROW(INDIRECT("1:"&$A2)))=0,ROW(INDIRECT("1:"&$A2))),COLUMNS($B2:B2)),"")

** array formulas need to be entered using the key
combination of CTRL,SHIFT,ENTER (not just ENTER).
Hold down both the CTRL key and the SHIFT key
then hit ENTER.

Copy down as needed then across until you get blanks.

If I understand the proposed code/formula, these look like basic "trial division" algorithms for factorization, which would work very well for small numbers like Tony Valko lists in his example. If you want to explore faster and more efficient algorithms (if your end goal is to factor much larger integers), you might want to do a little research into the Sieve of Eratosthenes (https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes ) or Wheel factorization (https://en.wikipedia.org/wiki/Wheel_factorization ) or any of the other prime factorization algorithms ( https://en.wikipedia.org/wiki/Integer_factorization ). Your question is not specifically limited to prime factors. Non-prime factors would be different combinations of the prime factors, so these prime factorization algorithms could make a good starting point.

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