How do I prove that If d/m.n and m^n=1 so there exist only one d'' and only one d' as d'/n and d" /m and d=d'.d"? Let [math]d(n)[/math] be the number of divisors of a natural number [math]n[/math]. How do you prove that [math]d(mn)=d(m)d(n) [/math] if [math]gcd(m, n)=1 [/math]?