Calculate Divisors

Calculate the proper divisors of positive natural numbers.

Usage

divisors(x)

Arguments

x

vector of positive whole numbers for which the divisors are to be returned.

Value

an integer vector containing the proper divisors in ascending order if x is a single number, otherwise a named list of such vectors. A prime number yields 1, and 1 itself yields integer(0) - its only divisor is 1, which is x itself and therefore not a proper one.

Details

Divisibility is a mathematical relationship between two integers. An integer is divisible by another integer if there is no remainder in the division. This function returns the proper divisors of x, i.e. all positive divisors excluding x itself. The number 11 is prime and has only the proper divisor 1, whereas the number 12 has the proper divisors 1, 2, 3, 4 and 6. In elementary number theory, the concept of divisibility is limited to natural numbers. The number of proper divisors can be determined with the function length().

See also

Other number.theory: GCD-LCM, digitSum(), factorize(), fibonacci(), isOdd(), isPrime(), primes()

Examples

divisors(786)
#> [1]   1   2   3   6 131 262 393

divisors(c(145, 786))
#> $`145`
#> [1]  1  5 29
#> 
#> $`786`
#> [1]   1   2   3   6 131 262 393
#> 

# the number of proper divisors
length(divisors(786))
#> [1] 7

# a prime has only one, and this one is at the integer limit
divisors(.Machine$integer.max)
#> [1] 1