AMC 10B 2024 (Problem 8)
Let be the product of all the positive integer divisors of . What is the units digit of ?
The number of positive divisors of is
The product of all positive divisors of is
The product of all positive divisors of is
The units digit of is the same as the units digit of .
The units digits of successive positive powers of follow the cycle
Since the cycle has length , the units digit of is .
The units digits of successive positive powers of follow the cycle
Since the cycle has length , the units digit of is .
(D)