2017 AMC 8 Problem 19
Attempt Problem 19 of the 2017 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 2017 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
For any positive integer the notation denotes the product of the integers through What is the largest integer for which is a factor of the sum:
Answer: D
Small hint:
Factor out of all three terms.
Big hint:
After factoring, count the powers of in and in .
Video solution:
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Written solution:
Factor out :
The exponent of in is , which equals The factor contributes four more factors of , so the total exponent is
Thus, D is the correct answer.
Problem 19 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
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2004 AMC 8
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- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
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- 2012 AMC 8
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