1974 AMC 12 Problem 26
Attempt Problem 26 of the 1974 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1974 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
The number of distinct positive integral divisors of excluding and is
none of these
Answer: C
Small hint:
Factor into powers of and
Big hint:
Choose each prime exponent independently from through then remove two divisors
Solution:
Because a divisor independently chooses each of three exponents from There are divisors. Excluding and leaves
Therefore, the correct answer is C.
Problem 26 in other years
- 1950 AMC 12
- 1951 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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