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Counting Factors

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

Printer Ink

Age 11 to 14 Short
Challenge Level

A small ink cartridge has enough ink to print $600$ pages.
Three small ink cartridges can print as many pages as two medium cartridges.
Three medium cartridges can print as many pages as two large cartridges.

How many pages can be printed using a large cartridge?

If you liked this problem, here is an NRICH task that 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.