
elementary number theory - What is meant by "evenly divisible ...
Aug 20, 2011 · "What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" Is it different from divisible?
Does ⋮ mean "is divisible by" in mathematical notation?
Nov 14, 2020 · Does ⋮ mean "is divisible by" in mathematical notation? Ask Question Asked 5 years, 1 month ago Modified 2 years, 2 months ago
How to know a number is divisible by a given number without using a ...
Oct 24, 2014 · For example, how do we decide intuitively that $11172686$ is divisible (or not) by $7$ or $13$? Moreover, I am interesting in knowing a simple rules or condition that a number is divisible by …
Divisibility by 7 - Mathematics Stack Exchange
The best way to test if a number is divisible by any other number is by deducting the number n times and check whether the remainder is divisible by n. for example 861-7n/7.
Divisibility of 9 trick: why does it work? [duplicate]
Jan 19, 2020 · I've been wondering ever since I learned about the divisibility of nine trick. Add up the sum of the digits. If the sum is a multiple of nine, the entire number is divisible by nine. If the sum is …
Proof of the divisibility rule of 11. - Mathematics Stack Exchange
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 …
How to prove the divisibility rule for $3\, $ [casting out threes]
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 …
divisibility - Is there a way to tell if a number is divisible by 4 if ...
Jul 11, 2019 · Robert Israel 's answer gives a method for determining whether a two-digit number is divisible by $4$, and the rule is saying that's essentially all you need. For example, if you want to …
Permutation and Combination with divisibility? - Mathematics Stack …
Dec 26, 2012 · An integer is divisible by $3$ if and only if the sum of its digits is divisible by $3$, so only the sets $\ {0,1,2,4,5\}$ and $\ {1,2,3,4,5\}$ will actually give you multiples of $3$. Every permutation …
elementary number theory - Divisibility Tests for Palindromes ...
I've found and proven the following extensions to palindromes of the usual divisibility rules for 3 and 9: A palindrome is divisible by 27 if and only if its digit sum is. A palindrome is divisible by 81 if and only if …