2020 AMC 8 Problem 17
Attempt Problem 17 of the 2020 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
How many factors of have more than factors? (As an example, has factors, namely and )
Answer: B
Small hint:
List or factor the divisors of
Big hint:
Only , primes, and have at most factors
Video solution:
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Written solution:
Since it has positive factors.
Among those factors, only and the primes and have fewer than three factors, while has exactly three. The other factors therefore have more than three factors.
Thus, the correct answer is B.
Problem 17 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
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- 1998 AMC 8
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