If a and b are integers and (2^a)(3^b) is a factor of 600^40, what is the largest possible value of ab?  Choices
A) a	B) 5a	C) 20a	D) 40a	E) 80a
(2^a)(3^b) is a factor of 600^40   We need to find the largest possible value of ab.   We know that 600 = 2^3*5^2*3^1   Therefore 600^40 will have one powers of 3 in it.   Hence in (2^a)(3^b), b has to 1   Therefore value of ab = a   Correct Option: a
<result>A</result>
If a and b are integers and (2^a)(3^b) is a factor of 600^40, what is the largest possible value of ab?