Maximum Number of Distinct Prime Factors

Number Theory Level 2

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

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

Dessert :

1 solution

Hemant Yadav
Feb 3, 2018

$3600=2^4.3^2.5^2$ $3600=2.2.2.2.3.3.5.5$

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