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18. Factors

A certain number has exactly eight factors including 1 and itself. Two of the other factors are 21 and 35. What is the number?
 

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Since both 21 and 35 are factors, then the known factors are:

1, 3, 5, 7, 21, 35

and since 3 and 5 are factors, then so is 15 and we now have

1, 3, 5, 7, 15, 21, 35

and the number must be the LCM of these, ie 105
 

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