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Minimum value with 75 (
Posted on 20141009
)
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)
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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 20141009 08:13:10
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