2005 AMC 12B Problems/Problem 21
Revision as of 18:43, 23 May 2018 by Scrabbler94 (talk | contribs) (→Solution: original solution wasn't quite correct since the prime factorization might not be p^1q^1r^2s^4. Improved solution using more standard notation and multiplicativity of d(n).)
Problem
A positive integer has
divisors and
has
divisors. What is the greatest integer
such that
divides
?
Solution
We may let , where
is not divisible by 7. Using the fact that the number of divisors function
is multiplicative, we have
. Also,
. These numbers are in the ratio 3:4, so
.
See also
2005 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 20 |
Followed by Problem 22 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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