Is a decimal number system the best to grasp mathematics?

Question

I am often amazed by how accurate a decimal numeral system is to describe the mathematics world. A lot of things feel very logical like the result of any multiplication by 5 will always end with a 0 or a 5. Or this again with this rule: a number is divisible by 3 if the sum of its digits is divisible by 3.(*)

Bu I wonder if a binary or an octal or a hexadecimal wouldn't have more of these rules, that would make the understanding of maths even simpler. I guess we have the decimal numeral system in Occident because we have 10 fingers, but this doesn't mean it's the more efficient way of understanding all the maths logic. We use the Qwerty keyboard but it's not the most efficient keyboard around.

So in brief my questions are:

• Is the decimal numeral system the most efficient one to understand the mathematics rules and patterns of the universe, geometrics or simple multiplications/divisions?
• Is not, which one is the best?

*) I am only using this two rules as examples because I don't know a lot of others maths patterns like those one. But I would be interested in knowing if others patterns, (I am tempted to say, more important patterns), exists in other number systems, that don't exist in the decimal one.

Answer 1

the result of any multiplication by $5$ will always end with a $0$ or a $5$

Similar properties apply to a multiple of d in base b, if d divides b.

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a number is divisible by $3$ if the sum of its digits is divisible by $3$

Similar properties apply to a multiple of d in base b, if d divides $b-1$.

Answer 2

Not at all. The concept of using 10 as a baseline probably grew out of the practice of calculating using one's fingers

But all kinds of number systems have been used in place of the decimal system and with relative successes. For instance, our computers expressly use the binary system, and switch to hexadecimal for representation purposes.

Decimal system only remains that important to us mathematically, because we have had a history of using 10 as a base (for reasons explained on the wiki and elsewhere). So naturally, any computation we do using the decimal system seems like a breeze. I am sure similar rules like those for the digits 3 and 5 do exist for numbers in other base systems.

(please suggest edits before downvoting)