561

561 is a natural number that follows 560 and precedes 562. In mathematics it has several notable properties.

Its prime factorization is 3 × 11 × 17. It is the smallest Carmichael number, the first composite to satisfy a^(n−1) ≡ 1 (mod n) for every integer a that is coprime to n. It was described by Robert Carmichael in 1910. By Korselt's criterion, 561−1 = 560 is divisible by p−1 for p in {3, 11, 17}, which explains its Carmichael property. 561 is also a sphenic number (the product of three distinct primes) and the 33rd triangular number (561 = 33 × 34 / 2).

In numeral representations, 561 is written as 1000110001 in binary, 1061 in octal, and 0x231 in hexadecimal. In Roman numerals, it is DLXI.

In contemporary usage, 561 is the telephone area code for parts of southeastern Florida, including West Palm Beach, Boca Raton, Delray Beach, and surrounding areas.

As a calendar year, 561 CE falls in the early medieval period, a time of various regional developments across the Byzantine world and neighboring regions.