Multiple Number of Divisors in Multiple

The number 360 n 360 n has twice as many divisors as 360 360 does, where n n is a positive integer.

Find the minimum possible value of n . n.


Inspired by Pi Han Goh .


The answer is 7.

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2 solutions

Kushal Bose
Mar 5, 2018

360 has 24 factors and 360 *n has double i.e. 48 factors then just multiply a prime other than 2,3,5 then n=7

Giorgos K.
Mar 5, 2018

Mathematica

s=1;While[Length@Divisors[360s++]!=2Length@Divisors@360];s-1

7

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