if a=(2^3)(3^4)(5) and b is a positive integer, what is the greatest number values for b such that a/108b is an integer? show its solution.

Question

0

857

1

Guest Sep 19, 2014

+33665

+5

Best Answer

108 = 2²*3³ so a/(108b) = 2⁴*3⁴*5/⁽2²*3³*b) = 2*2*3*5/b

This is only an integer if b is 1 or 2 or 3 or 4 or 5 or 6 or 10 or 12 or 15 or 20 or 30 or 60

Alan Sep 19, 2014

Alan · Answer 1 · 2014-09-19T07:57:22

108 = 2²*3³ so a/(108b) = 2⁴*3⁴*5/⁽2²*3³*b) = 2*2*3*5/b

This is only an integer if b is 1 or 2 or 3 or 4 or 5 or 6 or 10 or 12 or 15 or 20 or 30 or 60