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Factor List

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

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?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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