If a and b are integers and (2^a)(3^b) is a factor of 180^40, what is the largest possible value of ab?  Choose the correct choice from the following answers
A) 2a
B) 5a
C) 20a
D) 40a
E) 80a
(2^a)(3^b) is a factor of 180^40   We need to find the largest possible value of ab.   We know that 180 = 2^2*5^1*3^2   Therefore 180^40 will have 2 powers of 3 in it.   Hence in (2^a)(3^b), b has to 2   Therefore value of ab = 2a   Correct Option: 2a
<result>A</result>
If a and b are integers and (2^a)(3^b) is a factor of 180^40, what is the largest possible value of ab?