Problem:
Let be the product of all the positive integer divisors of 42 . What is the units digit of ?
Answer Choices:
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Solution:
The prime factorization of 42 is . A divisor of 42 is determined by choosing whether or not to include each prime as a factor of the divisor, so there are divisors. Furthermore, the divisors can be formed into 4 pairs each of whose product is , and . Therefore . The value of the requested units digit of is the same as the units digit of , which is .
The problems on this page are the property of the MAA's American Mathematics Competitions