35 (number)

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34 35 36
Cardinal thirty-five
Ordinal 35th
(thirty-fifth)
Factorization 5 × 7
Divisors 1, 5, 7 , 35
Greek numeral ΛΕ´
Roman numeral XXXV
Binary 1000112
Ternary 10223
Senary 556
Octal 438
Duodecimal 2B12
Hexadecimal 2316

35 (thirty-five) is the natural number following 34 and preceding 36

Contents

In mathematics

35 is a tetrahedral number. Pyramid of 35 spheres animation.gif
35 is a tetrahedral number.
The 35 free hexominoes All 35 free hexominoes.svg
The 35 free hexominoes

35 is the sum of the first five triangular numbers, making it a tetrahedral number. [1]

35 is the 10th discrete semiprime () [2] and the first with 5 as the lowest non-unitary factor, thus being the first of the form (5.q) where q is a higher prime.

35 has two prime factors, (5 and 7) which also form its main factor pair (5 x 7) and comprise the second twin-prime distinct semiprime pair.

The aliquot sum of 35 is 13, within an aliquot sequence of only one composite number (35,13,1,0) to the Prime in the 13-aliquot tree. 35 is the second composite number with the aliquot sum 13; the first being the cube 27.

35 is the last member of the first triple cluster of semiprimes 33, 34, 35. The second such triple distinct semiprime cluster is 85, 86, and 87. [3]

35 is the number of ways that three things can be selected from a set of seven unique things, also known as the "combination of seven things taken three at a time".

35 is a centered cube number, [4] a centered tetrahedral number, a pentagonal number, [5] and a pentatope number. [6]

35 is a highly cototient number, since there are more solutions to the equation than there are for any other integers below it except 1. [7]

There are 35 free hexominoes, the polyominoes made from six squares.

Since the greatest prime factor of is 613, which is more than 35 twice, 35 is a Størmer number. [8]

35 is the highest number one can count to on one's fingers using senary.

35 is the number of quasigroups of order 4.

35 is the smallest composite number of the form , where k is a non-negative integer.

In science

In other fields

See also

Related Research Articles

15 (fifteen) is the natural number following 14 and preceding 16.

20 (twenty) is the natural number following 19 and preceding 21.

21 (twenty-one) is the natural number following 20 and preceding 22.

70 (seventy) is the natural number following 69 and preceding 71.

34 (thirty-four) is the natural number following 33 and preceding 35.

46 (forty-six) is the natural number following 45 and preceding 47.

58 (fifty-eight) is the natural number following 57 and preceding 59.

62 (sixty-two) is the natural number following 61 and preceding 63.

91 (ninety-one) is the natural number following 90 and preceding 92.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

600 is the natural number following 599 and preceding 601.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.

6000 is the natural number following 5999 and preceding 6001.

In number theory, a branch of mathematics, a highly cototient number is a positive integer which is above 1 and has more solutions to the equation

216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.

177 is the natural number following 176 and preceding 178.

240 is the natural number following 239 and preceding 241.

888 is the natural number following 887 and preceding 889.

References

  1. "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  2. Sloane, N. J. A. (ed.). "SequenceA001358". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. Sloane, N. J. A. (ed.). "SequenceA001748". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  5. "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  6. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  7. "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  8. "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.