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12: It is divisible by 3 and by 4. [6] 324: it is divisible by 3 and by 4. Subtract the last digit from twice the rest. The result must be divisible by 12. 324: 32 × 2 − 4 = 60 = 5 × 12. 13: Form the alternating sum of blocks of three from right to left. The result must be divisible by 13. [7] 2,911,272: 272 − 911 + 2 = −637
12 (twelve) is the natural number following 11 and preceding 13.. Twelve is the 3rd superior highly composite number, [1] the 3rd colossally abundant number, [2] the 5th highly composite number, and is divisible by the numbers from 1 to 4, and 6, a large number of divisors comparatively.
Demonstration, with Cuisenaire rods, that 1, 2, 8, 9, and 12 are refactorable. A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that (). The first few refactorable numbers are listed in (sequence A033950 in the OEIS) as
Therefore, 12 is the greatest common divisor of 24 and 60. A 24-by-60 rectangular area can thus be divided into a grid of 12-by-12 squares, with two squares along one edge (24/12 = 2) and five squares along the other (60/12 = 5).
The first 15 superior highly composite numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 (sequence A002201 in the OEIS) are also the first 15 colossally abundant numbers, which meet a similar condition based on the sum-of-divisors function rather than the number of divisors. Neither ...
The prime numbers are precisely the atoms of the division lattice, namely those natural numbers divisible only by themselves and 1. [2] For any square-free number n, its divisors form a Boolean algebra that is a sublattice of the division lattice. The elements of this sublattice are representable as the subsets of the set of prime factors of n. [3]
divisible by the value of its φ function, which is 36. divisible by the total number of its divisors (12), hence it is a refactorable number. the angle in degrees of the interior angles of a regular pentagon in Euclidean space. palindromic in bases 11 (99 11), 17 (66 17), 26 (44 26), 35 (33 35) and 53 (22 53)
The smallest abundant number not divisible by 2 or by 3 is 5391411025 whose distinct prime factors are 5, 7, 11, 13, 17, 19, 23, and 29 (sequence A047802 in the OEIS). An algorithm given by Iannucci in 2005 shows how to find the smallest abundant number not divisible by the first k primes. [1]