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FactorInteger

FactorInteger[n]
gives a list of the prime factors of the integer n, together with their exponents.

does partial factorization, pulling out at most k distinct factors.

FactorInteger also works on rational numbers. The prime factors of the denominator are given with negative exponents. »

The last element in the list FactorInteger gives what is left after the partial factorization.

When necessary, a unit of the form , {I, 1}, or {-I, 1} is included in the list of factors.

Find prime factors and their exponents:

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FactorInteger threads itself element-wise over lists:

FactorInteger works with rational numbers:

Factor over Gaussian integers:

Find factorizations of numbers of the form

Display as an explicit product of factors:

Find primes that appear in prime factorization of

only to the first power:

Find all natural numbers up to 100 that are primes or prime powers:

The number of distinct factors of successive numbers:

The highest power of a prime in numbers up to 100:

The number of factors with Gaussian integers allowed:

Timings can increase rapidly and unpredictably with the size of the input: