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A factor is a portion of a quantity, usually an Integer or Polynomial. The determination of factors is called Factorization (or sometimes ``Factoring''). It is usually desired to break factors down into the smallest possible pieces so that no factor is itself factorable. For Integers, the determination of factors is called Prime Factorization. For large quantities, the determination of all factors is usually very difficult except in exceptional circumstances.
See also Divisor, Factorization, Greatest Prime Factor, Least Prime Factor, Prime Factorization Algorithms