SOLUTION: There are several positive integers that leave a remainder of 12 when they are divided into 192. Find the smallest three integers.
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Question 845376: There are several positive integers that leave a remainder of 12 when they are divided into 192. Find the smallest three integers.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Suppose 192 is divided by k. Then we can write 
, where 
, so 
. Hence k must be a factor of 180. Furthermore, k must be greater than 12, otherwise the remainder would be less than 12. The three smallest factors of 180 greater than 12 are 15, 18, and 20.
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