Factors / Factors of 1

Factors of 1

1

1 is the one number on this site with just a single factor: itself. It isn't prime (a prime needs exactly two divisors) and it isn't composite either, so it sits in its own category entirely. There's no factor pair to test for — trial division up to √1 = 1 has nothing to check, since the only candidate is 1 itself pairing with 1. Every other number's factor list on this site starts by including 1, precisely because 1 divides every integer evenly with no remainder; that's what makes it the multiplicative identity rather than an ordinary factor to hunt for. 1 is also, by convention, a perfect square (1² = 1), a perfect cube (1³ = 1), triangular, and the opening term of the Fibonacci sequence — degenerate cases that don't really apply to any other number quite the same way.