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multiplying on fingers also work with bases other than ten, why

At school I was shown how to multiply two intergers, both > 5 and <11 using the fingers on both hands.

Each hand used to represent one of the two numbers.

It works like this e.g 7x8= 56.

On the left hand count from 6 to 7 by folding down two fingers so that two are bend and three are not.

Then on the right hand count from 6 to 8 so that three are bend and two are not.

Count the number of straight fingers on each hand 3x2=6. this represents 6 units.

Count number of bent fingers on both hands and this represent the number of tens, five tens, or fifty.

So the answer is fifty plus six

The question is:

How come this works if we didnt have ten fingers and we counted for example in base 8 and had 8 fingers? If we counted in base 8 we would have 4 fingers on each hand and could multipy numbers from 5 to 8 using this method.