factors

Factorises an integer, preferably into prime factors.

Syntax

• factors(n)

  • n is an integer

Description

• If n is a positive integer greater than or equal to 2, factors(n) is the unique sorted list of prime numbers whose product is n. The result is the same as PrimeFactors(n).

• If n = 1, factors(n) = '(1). (On the other hand, PrimeFactors(1) = '().)

• If n = 0, factors(n) = '(0).

• If n is a negative integer, factors(n) is the same list as factors(abs(n)) but with the first element with a minus sign.

Notes

Unlike PrimeFactors, factors is defined also for non-positive integers. Moreover, while PrimeFactors(1) is the empty list (the unique list of prime numbers whose product is 1), factors(1) is '(1). For positive integers greater than or equal to 2, PrimeFactors and factors return the same list.

Unlike PrimeFactors, the elements of factors(n) might not be prime; indeed, 1, 0, and negative integers are not prime numbers.

Examples

factors(1)

1

factors(652358510)

2
5
17
3837403

factors(6454824420)

2
2
3
5
11
23
53
71
113

factors(4096)

2
2
2
2
2
2
2
2
2
2
2
2

factors(362014271)

362014271

factors(0)

0

factors(−652358510)

−2
5
17
3837403

See also

• PrimeFactors

• divisors