2005 Alabama ARML TST Problems/Problem 6: Difference between revisions
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<math>3240000=2^63^45^4</math>. We want to know how many numbers are in the form <math>2^{3a}3^{3b}5^{3c}</math>, <math>a\leq | <math>3240000=2^63^45^4</math>. We want to know how many numbers are in the form <math>2^{3a}3^{3b}5^{3c}</math>, <math>a\leq 2</math>,<math>b\leq 1</math>, <math>c\leq 1</math>; there are 12 such numbers, if we count 1 as a [[perfect cube]]. | ||
*[[2005 Alabama ARML TST]] | *[[2005 Alabama ARML TST]] | ||
*[[2005 Alabama ARML TST/Problem 5 | Previous Problem]] | *[[2005 Alabama ARML TST/Problem 5 | Previous Problem]] | ||
*[[2005 Alabama ARML TST/Problem 7 | Next Problem]] | *[[2005 Alabama ARML TST/Problem 7 | Next Problem]] | ||
Revision as of 13:50, 17 November 2006
Problem
How many of the positive divisors of 3,240,000 are perfect cubes?
Solution
. We want to know how many numbers are in the form 
, 
,
, 
; there are 12 such numbers, if we count 1 as a perfect cube.
