Problem
NT-B1-M09-P009 Oddness of \( au(225)\)
#9
★★☆☆☆ Level 2 of 5
Without listing all divisors, explain why \(\tau(225)\) is odd.
Check whether \(225\) is a square.
\(225=15^2\) is a square. A square has an odd number of positive divisors, because the divisor \(\sqrt{225}=15\) is unpaired. Hence \(\tau(225)\) is odd.
One may then check by formula: \(225=3^2\cdot5^2\), \(\tau=9\).