The taxman

In a very strange country, the tax system works as follows.
£1, £2, £3 up to £12 are available.
You pick an amount. You keep this amount, but the taxman takes any factors of it. You cannot pick any amount without a factor.
This continues until you can take no more money. The taxman gets any remaining money.
For example, you might play as follows:
In this example, you end with £22 and the taxman ends with £56.
Is it possible to get more money than the taxman? What is the most you can get?

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Tags: numbers, money
If you enjoyed this puzzle, check out Sunday Afternoon Maths XLII,
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