Number theory · Prime factorization · Coprimality · Divisor counting
Determine in how many ways the number \(441000\) can be written as a product of two factors \(m\) and \(n\) with
\[ m > 1, \qquad n > 1, \qquad \gcd(m,n) = 1 , \]
where the order of the factors is irrelevant, that is, the products \(m \cdot n\) and \(n \cdot m\) count as the same factorization.
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Serbian Municipal Competition 2007, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source