# Factors Command

##### Command Categories (All commands)

Factors[ <Polynomial> ]
Gives a list of lists of the type {factor, exponent} such that the product of all these factors raised to the power of the corresponding exponents equals the given polynomial. The factors are sorted by degree in ascending order.
Example:
Factors[x^8 - 1] yields {{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}.
Note: Not all of the factors are irreducible over the reals.
Factors[ <Number> ]
Gives matrix of the type \mathrm{\mathsf{ \left( \begin{array}{} prime_1 & exponent_1 \\ prime_2 & exponent_2 \\prime_3 & exponent_3 \\ \end{array} \right) }} such that the product of all these primes raised to the power of the corresponding exponents equals the given number. The primes are sorted in ascending order.
Example:
• Factors[1024] yields ( 2 10 ), since \mathrm{\mathsf{ 1024 = 2^{10} }}.
• Factors[42] yields \mathrm{\mathsf{ \left( \begin{array}{} 2 & 1 \\ 3 & 1 \\7 & 1 \\ \end{array} \right) }}, since \mathrm{\mathsf{ 42 = 2^1・3^1・7^1 }}.

Note: In the CAS View undefined variables can be used as input and the results are returned as proper matrices.
Example: Factors[a^8 - 1] yields \mathrm{\mathsf{ \left( \begin{array}{} a - 1 & 1 \\ a +1 & 1 \\a^2 + 1& 1 \\a^4 + 1& 1 \\ \end{array} \right) }}.
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