Problem
NT-B1-M09-P017 Product of Divisors of \(36\)
#17
★★★☆☆ Level 3 of 5
Find the product of all positive divisors of \(36\).
Use the formula \(n^{\tau(n)/2}\).
\(36=2^2\cdot3^2\), so \(\tau(36)=9\). The product of divisors is \(36^{9/2}=6\cdot36^4\). This is the exact value.
One may also list pairs \(1\cdot36\), \(2\cdot18\), \(3\cdot12\), \(4\cdot9\), and middle divisor \(6\).