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Karyoplasma ,

For divisibility by 13, take the last number, multiply by 4 and add to the rest.

For divisibility by 17, take the last number, multiply by 5 and subtract from the rest.

For divisibility by 19, take the last number, multiply by 2 and add to the rest.

In fact, you can adapt the method to check for divisibility by any prime number k.

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