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# 240 (number)

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 Title: 240 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 240 (number)

240 (two hundred [and] forty) is the natural number following 239 and preceding 241.

## 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.

## In other fields

240 is:

### 241 - 249

241 has its own article.

242 has its own article.

243 has its own article.

244 has its own article..

245 has its own article.

246 has its own article.

Two hundred [and] forty-seven 247 = 13·19, pentagonal number.
247 = 50123 - 49876, and is the smallest number which can be expressed as the difference between two integers such that together, they contain all digits 0-9.

• Sometimes (e.g. when it is used in a URL), 247 is used as an alternative to 24/7, an abbreviation which means "24 hours a day, 7 days a week".
• Approximate number of acres in a square kilometer.

Two hundred [and] forty-eight 248 = 23·31, nontotient, untouchable number, refactorable number; E8 has complex dimension 248.

• The number 248 is also the commandments in the Torah.

Two hundred [and] forty-nine 249 = 3·83, Blum integer

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