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Minimum value with 75 (Posted on 2014-10-09) Difficulty: 3 of 5
N is a positive integer such that:

(A) N is a multiple of 75, and:
(B) N has precisely 75 positive integer divisors including 1 and itself.

What is the minimum value of N/75?.

No Solution Yet Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution D2 (spoiler) Comment 1 of 1
75=5*5*3

So a number has 75 divisors if its prime factorization is of the form x^4 * y^4 * z^2

The smallest such number is 2^4 * 3^4 * 5^2, which happily is a multiple of 75

So, N/75 = 2^4 * 3^3 = 432

  Posted by Steve Herman on 2014-10-09 08:13:10
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