1. The smallest positive integer n with 24 divisors considering 1 and n as divisors is
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By: anil on 05 May 2019 02.41 am
For any given number, that can be represented as $$ A^{x} imes B ^ {y} $$, etc The number of factors is denoted by (x+1) x ( y+1), etc 360 = $$ 2 ^ {3} imes 3 ^ {2} imes 5^ {1}$$ So the number of factors = (3 +1) x (2+ 1) (1+ 1) = 4x3x2 = 24 For 240, it is $$ 2 ^ {4} imes 3 ^ {1} imes 5^ {1}$$ Number of factors = 5 x 2 x 2 = 20 only
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