perplexus.info :: Just Math : Minimum value with 75

Minimum value with 75 (Posted on 2014-10-09)

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?.

See The Solution Submitted by K Sengupta

Rating: 3.3333 (3 votes)

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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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