# factor invocation (GNU Coreutils 9.0)

Next: numfmt invocation, Up: Numeric operations [Contents][Index]

### 26.1 factor: Print prime factors

`factor`

prints prime factors. Synopses:

factor [number]… factor option

If no `number`

is specified on the command line, `factor`

reads numbers from standard input, delimited by newlines, tabs, or spaces.

The `factor`

command supports only a small number of options:

- ‘
`--help`

’ - Print a short help on standard output, then exit without further processing.
- ‘
`--version`

’ - Print the program version on standard output, then exit without further processing.

If the number to be factored is small (less than *2^{127}* on typical machines), `factor`

uses a faster algorithm. For example, on a circa-2017 Intel Xeon Silver 4116, factoring the product of the eighth and ninth Mersenne primes (approximately *2^{92}*) takes about 4 ms of CPU time:

$ M8=$(echo 2^31-1 | bc) $ M9=$(echo 2^61-1 | bc) $ n=$(echo "$M8 * $M9" | bc) $ bash -c "time factor $n" 4951760154835678088235319297: 2147483647 2305843009213693951 real 0m0.004s user 0m0.004s sys 0m0.000s

For larger numbers, `factor`

uses a slower algorithm. On the same platform, factoring the eighth Fermat number *2^{256} + 1* takes about 14 seconds, and the slower algorithm would have taken about 750 ms to factor *2^{127} - 3* instead of the 50 ms needed by the faster algorithm.

Factoring large numbers is, in general, hard. The Pollard-Brent rho algorithm used by `factor`

is particularly effective for numbers with relatively small factors. If you wish to factor large numbers which do not have small factors (for example, numbers which are the product of two large primes), other methods are far better.

An exit status of zero indicates success, and a nonzero value indicates failure.

Next: numfmt invocation, Up: Numeric operations [Contents][Index]