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.

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, Let's …

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 a necessary …

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 the 4 rule.

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 memorize beca...

Feb 23, 2020 · Divisibility by 73 and by 137 is tested with alternating sums of four-digit groups. The number 137 is the largest prime that can be tested using simple sums of alternating sums involving …

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 k-digit blocks …

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 number is

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 11, then …

Jan 17, 2018 · Divisibility rules based on modulo arithmetic. Ask Question Asked 7 years, 11 months ago Modified 4 years, 5 months ago