115500 needs positive divisor

Number Theory Level 3

The total number of proper positive divisors of 115500 is

Note: The term "proper divisors" excludes the number itself.

The answer is 95.

1 solution

Aditya Raut
Jul 13, 2014

The number given is

$115500 = 100\times 11 \times 105 = 2^2.3.5^3.7. 11$

Thus the number of factors is $3\times 2\times 4\times 2\times 2 = 96$ and this includes the number itself. But in PROPER divisors, we have to exclude the number itself, hence the answer is $\boxed{95}$

Where do you get the $3\times 2 \times 4 \times 2\times 2=96$ ? :o

Astro Enthusiast - 6 years, 10 months ago

Precious: Notice that the factor 2 can be included 0, 1 or 2 times, which is 3 possibilities. Likewise, the factor 3 can be included 0 or 1 times, which is 2 possibilities. 5 can be included from 0 to 3 times, which is 4 possibilities. And so on.

Bill Bell - 6 years, 10 months ago

$Response$ to $Astro$ $Enthusiast$ : Actually there is a formula that for every positive composite number $N$ and its distinct prime factors $a,b,c,d.........$ with $p,q,r,s.............$ being the indices of $a,b,c,d........$ .

$N=a^{p} \times b^{q} \times c^{r} \times d^{s} \times ............$

Then total factors of $N=(p+1)(q+1)(r+1)(s+1)...................$

Abhisek Mohanty - 6 years, 2 months ago

Proper divisors only excludes the number itself, but include 1. So the answer should be 96-1=95.

I've updated the answer to 95.

Calvin Lin Staff - 6 years, 11 months ago

number of factors and number Proper divisors are equal, isn't??

Arun AR - 6 years, 10 months ago

The correct answer is 94

Hariom Yadav - 3 years, 5 months ago

Yes the answer should be 96

akhilesh agrawal - 6 years, 11 months ago

115500 needs positive divisor

The answer is 95.

1 solution

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