240 (two hundred [and] forty) is the
natural number following
239 and preceding
241.
Mathematics
240 is a
pronic number, since it can be expressed as the product of two consecutive integers,
15 and
16.[1] It is a
semiperfect number,[2] equal to the concatenation of two of its proper divisors (24 and 40).[3]
It is also a
highly composite number with 20 divisors in total, more than any smaller number;[4] and a
refactorable number or tau number, since one of its divisors is 20, which divides 240 evenly.[5]
240 is the
aliquot sum of only two numbers: 120 and 57121 (or 2392); and is part of the 12161-aliquot tree that goes: 120, 240, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 0.
It is the smallest number that can be expressed as a sum of consecutive primes in three different ways:[6]
240 is
highly totient, since it has thirty-one totient answers, more than any previous integer.[7]
It is palindromic in bases 19 (CC19), 23 (AA23), 29 (8829), 39 (6639), 47 (5547) and 59 (4459), while a
Harshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15 (and 73 other bases).
240 is the number of distinct solutions of the
Soma cube puzzle.[11]
There are exactly 240 visible pieces of what would be a
four-dimensional version of the
Rubik's Revenge — a Rubik's Cube. A Rubik's Revenge in three dimensions has 56 (64 – 8) visible pieces, which means a Rubik's Revenge in four dimensions has 240 (256 – 16) visible pieces.