Editing Divisibility rule (section)

===Divisibility by 3 or 9===
First, take any number (for this example it will be 492) and add together each digit in the number (4 + 9 + 2 = 15). Then take that sum (15) and determine if it is divisible by 3. The original number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3 (or 9).

Adding the digits of a number up, and then repeating the process with the result until only one digit remains, will give the [[remainder]] of the original number if it were divided by nine (unless that single digit is nine itself, in which case the number is divisible by nine and the remainder is zero).

This can be generalized to any [[List of numeral systems#Standard positional numeral systems|standard positional system]], in which the divisor in question then becomes one less than the [[radix]]; thus, in [[duodecimal|base-twelve]], the digits will add up to the remainder of the original number if divided by eleven, and numbers are divisible by eleven only if the digit sum is divisible by eleven.

'''Example.'''
# 492 (The original number)
# 4 + 9 + 2 = 15 (Add each individual digit together)
# 15 is divisible by 3 at which point we can stop. Alternatively we can continue using the same method if the number is still too large:
# 1 + 5 = 6 (Add each individual digit together)
# 6 ÷ 3 = 2 (Check to see if the number received is divisible by 3)
# 492 ÷ 3 = 164 (If the number obtained by using the rule is divisible by 3, then the whole number is divisible by 3)