How many zeros are at the end of (100!)(200!)(300!) when multiplied out?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many zeros are at the end of (100!)(200!)(300!) when multiplied out?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
147
How many zeros are at the end of (100!)(200!)(300!) when multiplied out?
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