The test for base-10 divisibility by 11 has a straightforward analogue in other bases. For example, in base 12, 756899 is divisible by 13 because 7+6+9 = 5+8+9.

Mar 26, 2013 · The induction methods is nice because it provides an insight into why this divisibility rule works. However, AFAICS, it only shows that the digit-sum being divisible by 3 is …

I always find myself doing tests with binary numbers (without a calculator, I'm now developing automatas) and I've always asked myself if there was a fast trick to check whether a generic …

Dec 6, 2018 · If A has a divisibility rule, then R n A can exclude the last n digits and use the rule for A. Given these rules, 12 rules should work for base 10 as a combination of the 3 rule and …

Sep 27, 2021 · We know, A number is divisible by $11$ if the difference of the sum of the digits in the odd places and the sum of the digits in the even places is divisible by $11$. For example, …

There is also a similar less known trick for divisibility by 11. Since $10 = -1 \mod 11$, if you add the digits of a number in reverse order, alternating signs, and get something that is divisible by …

Nov 12, 2024 · Using these divisibility rules, one can check if a number is divisible by any prime divisor of $10^k-1$ or $10^k+1$ by checking if the sum or alternating sum, respectively, of its …

Jan 17, 2018 · Divisibility rules based on modulo arithmetic. Ask Question Asked 7 years, 11 months ago Modified 4 years, 4 months ago

What is the fastest known way for testing divisibility by 7? Of course I can write the decimal expansion of a number and calculate it modulo 7, but that doesn't give a nice pattern to …

Oct 3, 2016 · The purpose of divisibility tricks is meant only to apply to the numbers of base 10, effectively ignoring the true value of the number and focusing plainly on the external digits …