jmc

Because 120 is a multiple of 40, every divisor of 40 is also a divisor of 120. Thus, if a number is a divisor of 40, it is automatically a factor of 120 too. The problem is asking "How many positive integers are factors of 40?". Listing out the factors, we get $$1,2,4,5,8,10,20,40.$$Counting, we see there are $\boxed{8}$ positive integers.