The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.  Of these, the $\boxed{3}$ factors 10, 25 and 50 have two digits and are factors of 150 as well.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many positive two-digit integers are factors of both 100 and 150?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
How many positive two-digit integers are factors of both 100 and 150?
test