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Q: What prime number must be multiplied to 12 to make it 132?
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How many prime numbers must be multiplied to make 2400?

Three distinct prime factors, eight total.


What is the smallest number that 7800 must be multiplied by to give a square number?

Well, isn't that a happy little question! To find the smallest number that 7800 must be multiplied by to give a square number, we need to break down 7800 into its prime factors. Once we have those, we can pair them up to form perfect squares. By doing this, we can see that the smallest number 7800 must be multiplied by to give a square number is 3, because when we pair up all the prime factors, we have every factor in pairs except for one factor of 3. And just like that, we've painted a beautiful solution!


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