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'Weekly Problem 48 - 2010' printed from http://nrich.maths.org/

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When Tina chose a number N and wrote down all of its factors, apart from $1$ and N, she noticed that the largest of the factors in the list was $45$ times the smallest factor in the list. How many numbers N could Tina have chosen for which this is the case?
 
 
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This problem is taken from the UKMT Mathematical Challenges.

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