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### Why is 12 Such a Popular Number?

Why is 12 Such a Popular Number?

Have you noticed how popular the number 12 is? There's 12 of anything in a dozen, 12 inches in a foot, 12 months in a year, 12 hours in a day. You can probably find more examples. Why is 12 used so much in everyday life? I mean, we have 10 fingers, so you would expect 10 to be the most popular number. But it's not.

A prime number has no divisors, but 12 has 4 of them (2, 3, 4, 6). That's twice as many as 10, which only has 2 divisors (2, 5). Perhaps 12 became popular in everyday life because there are more ways to divide 12 objects into equal sized pieces. Equal size is the key thing here, because that's exactly what you need for sharing.

If the operation D takes an integer and gives you the number of its divisors then D(10)=2, D(12)=4 and D(p)=0 for any prime integer p. Of course, when we talk about the number of divisor we don't count 1 and the number itself. All numbers have these two trivial divisors, so we don't count them.

A couple of interesting questions..

D(10) is a divisor of 10 and D(12) is a divisor of 12. This is not true in general. I wonder what the condition is for D(n) to be a divisor of n?

The two neighbors of 12 (11 and 13) are both prime numbers, which means they have no divisors. So, if p and p+2 are any prime pair is it true that D(p+1) is "large"?

Content written and posted by Ken Abbott abbottsystems@gmail.com