Divisibility and Extensibility

I love 12, and so did the Indo-Europeans. There are Twelve Olympian Gods, Twelve high gods of the Aesir, Twelve Roman Gods. There are twelve months in a year. There are twelve hrs in a half day. My favorite is the notion of natural divisors. This gets to my point. Log is base 10. Centrigrade scales use that. We count in 10s because we have 10 fingers, 10 toes. Orders of magnitude are simple, move the decimal (get it?) over. I've been in love with this point for years but it seems at least the math geeks may have beaten me to the punch. A tip of the hat to this gentleman for his mathematical only treatment but...

The dodecahedron fills space nicely. . My time rolling dice for Dungeons and Dragons told me I really loved weapons that inflicted 1-12 Hit Points of damage. The shape was just so nice and spinning it was so easy and natural.

So why do I care about 12? Or its divisors: 2, 3, 4, 6. Because that composite's constituent parts can be recombined, multiplied and worked with to come up with more PRIMES faster! get to 11 from 10s divisors (other than 10 and 1). 5+2+2+2. Get there with 12s divisors. 2+3+6. 4 to 3. 12s get there faster. Now 13. 5+2+2+2+2. with 12s - 6+4+3. that is 5-3, twelve wins. Ok. 5. that one is easier with 10's divisors. 5 vs 2+3. 1 vs 2. 10 wins. Fibonacci sequence doesn't have a number that is easier to get to with 10s parts. 12s parts always win. I'll post the table soon.
So if you want to build up to many different solutions (numbers in a sequence in this case, but be creative and think of how you'd apply this to Construction, software, analytics, etc), find the right number to divide by (call this your base structure), divide it into its foundational blocks and recombine (extend) into all the goodness that comes from it AT THE LEAST COST!