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Is there an efficient way to work out how many factors a large number has?

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Stamp Collecting

Age 11 to 14 Short Challenge Level:


Last week, Tom and Sophie bought some stamps for their collections.
Each stamp Tom bought cost him £1.10, whilst Sophie paid 70p for each of her stamps.

Between them they spent exactly £10.

How many stamps did they buy in total?


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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.