Statement How many positive divisors does 120012001200 have? Solution Factor it: 1200=24⋅3⋅52.1200 = 2^4\cdot 3\cdot 5^2.1200=24⋅3⋅52. Adding 111 to each exponent and multiplying: (4+1)(1+1)(2+1)=5⋅2⋅3=30.(4+1)(1+1)(2+1) = 5\cdot 2\cdot 3 = \boxed{30}.(4+1)(1+1)(2+1)=5⋅2⋅3=30.