Maximum Number of Distinct Prime Factors

N N is positive integer which has 3600 3600 positive divisors (including 1 1 and itself).

Find the maximum number of distinct prime factor(s) of N N .


Dessert :

  • Generalize this for any positive integer d d replacing 3600 3600 .


The answer is 8.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Hemant Yadav
Feb 3, 2018

3600 = 2 4 . 3 2 . 5 2 3600=2^4.3^2.5^2 3600 = 2.2.2.2.3.3.5.5 3600=2.2.2.2.3.3.5.5

Since, 3600 3600 can be written as product of at most 8 8 numbers greater than 1, we can say that N N can have at most 8 8 prime factors

N does not equal 3600. 3600 is the number of divisors. The answer you gave is based on 3600 not N

Greg Grapsas - 2 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...