Divisibility Rules for Bases other than - Mathematics Stack Exchange I still remember the feeling, when I learned that a number is divisible by $3$, if the digit sum is divisible by $3$ The general way to get these rules for the regular decimal system is asked answered here: Divisibility rules and congruences Now I wonder, what divisibility rules an alien with $12$ (or $42$) fingers would come up with?
Divisibility Tests in Various Bases - Mathematics Stack Exchange One thing that has been on my mind lately is why a number of simple rules work for determining if some large number is a multiple of some other number In base 10, I was taught the following divisibility rules: 2: Ends with an even digit; 3: Sum all the digits If that number is a multiple of 3, so is the whole number
elementary number theory - Divisibility rule for large primes . . . 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 four or fewer digits
Proof of the divisibility rule of 17. - Mathematics Stack Exchange Recognize that divisibility by a 17 means you can write the number as 17n for a positive integer n So our statement is if x-5y=17n then 10x + y = 17m, where x,y,m,n are positive integers Assume x - 5y = 17n Now we try to get the left-hand side to look like our original number First multiply both sides by 10
finding missing digits using divisibility rules 1) Divisibility by eleven means the sum of the even digits minus the sum of the odd digits is a multiple of eleven So x9938945498y6542054345z divisible by 11 means x + 9 +8 +4 + 4 + 8 + 6 + 4 + 0 + 4 + z = 9 + 3 + 9 + 5 + 9 + y + 5 + 2 + 5 + 3 + 5 + 11k
Divisibility criteria for - Mathematics Stack Exchange A number is divisible by $2$ if it ends in $0,2,4,6,8$ It is divisible by $3$ if sum of ciphers is divisible by $3$ It is divisible by $5$ if it ends $0$ or $5$ These are simple criteria for divisibility I am interested in simple criteria for divisibility by $7,11,13,17,19$
Why do some divisibility rules work only in base 10? 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 itself Sort of like when dividing by 3, 12 fits perfectly base 10, but in base 3 [5] does not