This is the table of 144 numbers that Emily, and millions like her, are drilled on every week at school. The numbers have been colour-coded to their lowest prime factor according to Emily’s scheme.
![timestable](https://www.archinterface.co.uk/wp-content/uploads/2018/02/timestable-292x300.jpg)
Each number is repeated 2.5 times on average and some numbers appear 6 times. The table only contains the safe, friendly and boring numbers.
Here is another table of 144 numbers with each appearing only once.
![emilys timestable](https://www.archinterface.co.uk/wp-content/uploads/2018/02/emilys-timestable-292x300.jpg)
We can see the odd numbers, even numbers and multiples of three more clearly than before – and now we also have all the interesting oddish numbers.
In both tables, only the primes in the top row need distinct colour-coding to highlight the other numbers in the table where that prime is the lowest factor. The tables have a square format and so, by definition, the highest number in the bottom-right corner is the square of the number in the top-right corner. The fact that this is true for both tables tells us something about the relationship between addition and multiplication.
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