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Proper Factors
Age 16 to 18
Challenge Level 
It might be easier to start by thinking about the total number of factors (so include $1$ and $N$).
How many factors are there of:
- $3$
- $3 \times 5 = 15$
- $3^2 \times 5 = 45$?
Can you spot any patterns to help you find the total number of factors of $3^2 \times 5^3$?
What are the total number of factors of $3^m \times 5^n$?.
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