In Mathematics
With 20 divisors total (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240), more than any previous number, 240 is a highly composite number, and it is also a refactorable number or tau number, since it has 20 divisors and 20 divides 240. And since it has 31 totient answers, more than any previous integer, 240 is a highly totient number.
240 is a semiperfect number.
240 can be expressed as a sum of consecutive primes in two different ways: 240 = 53 + 59 + 61 + 67 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43. It can also be expressed as the product of two consecutive integers, 15 and 16, thus 240 is a pronic number.
Also, being divisible by the sum of its digits, 240 is a Harshad number, and not only that, it is also a concatenation of two of its proper divisors (see Sloane's A50480).
E8 has 240 roots.
There are 240 distinct solutions of the Soma cube puzzle.
Read more about this topic: 240 (number)
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