Math Visualization: Factors

Simon is visualizing factors in GeoGebra.

This graph visualizes how many factors a number has. If a number is higher on the graph than any number to the left of it, it’s a highly composite number:

And the graph below is the same graph, just zoomed out a lot on the x axis and a bit on the y axis, resulting in numbers subdividing neatly into rows, according to the number of divisors:

Fun fact: the odd rows have fewer numbers than the even rows. That’s because the only numbers with an odd number of factors are square numbers! Also, the only number in the first row is one itself. This is because all other numbers have at least two factors: one and the number itself.

And then Simon hopped into GeoGebra and showed me a way to visualize Superior Highly Composite Numbers:

That’s why there are more than one Superior Highly Composite Numbers, because epsilon can be different. This is just a way to make a number smaller and increasingly smaller if the number is bigger. I would have probably used a different way, but it’s just the definition of SHCNs…

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