Prime Factorization of Integers

Compute the prime factorization(s) of integer(s) n.

Factorize(n)

Arguments

n

vector of integers to factorize.

Details

works via Primes, currently in a cheap way, sub-optimal for large composite \(n\).

Value

A named list of the same length as n, each element a 2-column matrix with column "p" the prime factors and column~"m" their respective exponents (or multiplities), i.e., for a prime number n, the resulting matrix is cbind(p = n, m = 1).

Author

Martin Maechler, Jan. 1996.

See also

GCD, LCM, Primes, IsPrime, Divisors

For factorization of moderately or really large numbers, see the gmp package, and its factorize() (which is ~20x faster!).

Examples

 Factorize(47)
#> $`47`
#>       p m
#> [1,] 47 1
#> 
 Factorize(seq(101, 120, by=2))
#> $`101`
#>        p m
#> [1,] 101 1
#> 
#> $`103`
#>        p m
#> [1,] 103 1
#> 
#> $`105`
#>      p m
#> [1,] 3 1
#> [2,] 5 1
#> [3,] 7 1
#> 
#> $`107`
#>        p m
#> [1,] 107 1
#> 
#> $`109`
#>        p m
#> [1,] 109 1
#> 
#> $`111`
#>       p m
#> [1,]  3 1
#> [2,] 37 1
#> 
#> $`113`
#>        p m
#> [1,] 113 1
#> 
#> $`115`
#>       p m
#> [1,]  5 1
#> [2,] 23 1
#> 
#> $`117`
#>       p m
#> [1,]  3 2
#> [2,] 13 1
#> 
#> $`119`
#>       p m
#> [1,]  7 1
#> [2,] 17 1
#>