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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:


Print a short help on standard output, then exit without further processing.


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

Factoring the product of the eighth and ninth Mersenne primes takes about 30 milliseconds of CPU time on a 2.2 GHz Athlon.

M8=$(echo 2^31-1|bc)
M9=$(echo 2^61-1|bc)
n=$(echo "$M8 * $M9" | bc)
/usr/bin/time -f %U factor $n
4951760154835678088235319297: 2147483647 2305843009213693951

Similarly, factoring the eighth Fermat number 2^{256}+1 takes about 20 seconds on the same machine.

Factoring large numbers is, in general, hard. The Pollard 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.

If factor is built without using GNU MP, only single-precision arithmetic is available, and so large numbers (typically 2^{64} and above) will not be supported. The single-precision code uses an algorithm which is designed for factoring smaller numbers.

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