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# 249 (number)

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### 249 (number)

Template:Infobox 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

Two hundred [and] forty-one has its own article.

Two hundred [and] forty-two has its own article.

Two hundred [and] forty-three has its own article.

Two hundred [and] forty-four 244 = 22·61, nontotient, noncototient, self number.

Two hundred [and] forty-five has its own article.

Two hundred [and] forty-six 246 = 2·3·41, sphenic number, nontotient, untouchable number.

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 (when it is a URL, etc.) may use "247" as an alternate to 24/7, it is an abbreviation which stands for "24 hours a day, 7 days a week".

Two hundred [and] forty-eight 248 = 23·31, nontotient, untouchable number, refactorable number; E8 has complex dimension 248. The number 248 is also the Gematria value for the Hebrew letters Ramach (Resh Mem and Het), traditionally depicted as the number of organs in the human body, and the number of positive commandments in the Torah.

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

Template:Integers

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