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The result must be divisible by 11. 627: 62 − 7 = 55 = 5 × 11. Add 10 times the last digit to the rest. The result must be divisible by 11. (Works because 99 is divisible by 11). 627: 62 + 70 = 132: 13 + 20 = 33 = 3 × 11. If the number of digits is even, add the first and subtract the last digit from the rest. The result must be divisible ...
{11, 22, 33, 44, 55, 66, 77, 88, 99}. All palindromic numbers with an even number of digits are divisible by 11. [1] There are 90 palindromic numbers with three digits (Using the rule of product: 9 choices for the first digit - which determines the third digit as well - multiplied by 10 choices for the second digit):
Two properties of 1001 are the basis of a divisibility test for 7, 11 and 13. The method is along the same lines as the divisibility rule for 11 using the property 10 ≡ -1 (mod 11). The two properties of 1001 are 1001 = 7 × 11 × 13 in prime factors 10 3 ≡ -1 (mod 1001) The method simultaneously tests for divisibility by any of the factors ...
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
Demonstration with Cuisenaire rods of the amicability of the pair of numbers (220,284), the first of the series.. In mathematics, the amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number.
Hailstone sequences can be computed by the 2-tag system with production rules a → bc , b → a , c → aaa . In this system, the positive integer n is represented by a string of n copies of a , and iteration of the tag operation halts on any word of length less than 2.
An integer is even if it is divisible by 2, and odd if it is not. [1] For example, −4, 0, and 82 are even numbers, while −3, 5, 7, and 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201.
Digit sums and digital roots can be used for quick divisibility tests: a natural number is divisible by 3 or 9 if and only if its digit sum (or digital root) is divisible by 3 or 9, respectively. For divisibility by 9, this test is called the rule of nines and is the basis of the casting out nines technique for checking calculations.