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

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.*

View the previous week's solution