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6: It is divisible by 2 and by 3. [6] 1,458: 1 + 4 + 5 + 8 = 18, so it is divisible by 3 and the last digit is even, hence the number is divisible by 6. Sum the ones digit, 4 times the 10s digit, 4 times the 100s digit, 4 times the 1000s digit, etc. If the result is divisible by 6, so is the original number.
96 as the difference of two squares (in orange). 96 is: an octagonal number. [1] a refactorable number. [2] an untouchable number. [3] a semiperfect number since it is a multiple of 6. an abundant number since the sum of its proper divisors is greater than 96. the fourth Granville number and the second non-perfect Granville number.
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
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.
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]
First, the digits of the number being tested are grouped in blocks of three. The odd numbered groups are summed. The sum of the even numbered groups is then subtracted from the sum of the odd numbered groups. The test number is divisible by 7, 11 or 13 iff the result of the summation is divisible by 7, 11 or 13 respectively. [2] [3] Example:
I was hardly ever what you would call popular. People who attend Shakespeare camp rarely are. But in my teens and 20s, I always had a robust group of friends who shared my weirdness in differing ways.
In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not. The former names are traditional ones, derived from ancient Greek mathematics ; the latter have become common in recent decades.