Tax file numbers (TFNs) are so much an everyday element when dealing with tax and the ATO that many practitioners and ordinary self-preparers won’t give it a second thought when tax return software responds with an “invalid” when a TFN is entered.

The common thought will be that it’s human error, so naturally one’s first reaction will be to check the numbers your client gave you, followed by making sure you c-a-r-e-f-u-l-l-y re-enter the numbers.

Most of the time the problem will be fixed and it’s business as usual, but here’s a passing thought — how does the tax return software know what is, and what is not, a valid TFN?

And remember, its validity or otherwise is not dependant on matching those numbers with someone’s name and/or birthday and/or address and so on. These identifiers are used to cross-check a person’s identity of course, but the initial validity of a TFN is known via another factor — the “TFN algorithm”.

This verification algorithm is embedded in each unique TFN and is also known as a check digit algorithm. Essentially the veracity of the sequence of numbers that make up each TFN is based on the fact that one of the digits (the last one in this case) depends on the other digits.

It’s not magic, but just to maintain the fun let’s take an element from the magician’s playbook… think of a number between 10 and 12, and keep that in mind.

To make the algorithm work, a fixed weighting is applied to each number of the TFN. In order from the left, these weightings are 1 4 3 7 5 8 6 9 10. As with a lot of these things, the rest is best explained using an example.

Let’s take the following TFN; 123 456 782. Now multiply each digit by the weightings, in order.

1 x 1 = 1, 2 x 4 = 8, 3 x 3 = 9, 4 x 7 = 28, 5 x 5 = 25, 6 x 8 = 48, 7 x 6 = 42, 8 x 9 = 72 and 2 x 10 = 20.

Now, add those results together. 1 + 8 + 9 + 28 + 25 + 48 + 42 + 72 + 20 = 253. Now, remember that number you were keeping in mind? If the total you arrived at (in this case, 253) is a multiple of 11, you’ve got yourself a true TFN.

To check for yourself, try the above with your own TFN.

The check digit algorithm is not generally disclosed and was kept in the ATO’s vault for decades, but in more modern times the algorithm has had to be shared with many external entities such as software developers, who are generally required to sign a confidentiality agreement.