How many divisors does 55,125 have?

musakhanyan-dis · ‎Sep 06, 2003

How many divisors does 55,125 have?
Is there any intelligent way solve this problem?
By using combinatorial methods...

IRstuff · ‎Sep 06, 2003

On 9/6/2003 8:27:29 PM, musakhanyan wrote:
>How many divisors does 55,125
>have?
>Is there any intelligent way
>solve this problem?
>By using combinatorial
>methods...

Since it ends in 5 and digits sum to 18, you know that there's at least 3 and 5 as factors

TTFN,
Eden

TKHunny · ‎Sep 06, 2003

Prime Factorization:

55125 = 3²�5³�7²

There's your hint. How many different ways can you rearrange these factors and produce unique results that are factors of 55125?

Additionally, you don't have to look any higher that sqrt(55125). Why is that?

pkalford-disabl · ‎Sep 07, 2003

Allow me to build upon what Tkh has given you. Although I am generally opposed to working out problems, having taught this a number of times I find students always have trouble with it.
Because 55125 = 3²·5³·7² then any factor of 55125 must be of the form 3^a·5^b·7^c where 0 £ a £ 2, 0 £ b £ 3, and 0 £ c £ 2.. In essence we need to count the number of triples (a,b,c) that satisfy those conditions. For (0,0,0) we get the factor 1, for (2,3,2) we get the factor 55125.
I will tell the end result is 36. How did we get this number?

PKA