35 (number)

Natural number

| ← 34  | 35 |  36 →

|
|

← 30 31 32 33 34 35 36 37 38 39 →

* List of numbers
* Integers

← 0 10 20 30 40 50 60 70 80 90 →

Cardinal| thirty-five
Ordinal| 35th
(thirty-fifth)
Factorization| 5 × 7
Divisors| 1, 5, 7, 35
Greek numeral| ΛΕ´
Roman numeral| XXXV, 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.

## In mathematics

[edit]

35 is a tetrahedral number. 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 ( 5 × 7 {\displaystyle 5\times 7} )[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  x − φ ( x ) = 35 {\displaystyle x-\varphi (x)=35} 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  35 2 + 1 = 1226 {\displaystyle 35^{2}+1=1226} 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  6 k + 5 {\displaystyle 6k+5} , where k is a non-negative integer.

## References

[edit]

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.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ Sloane, N. J. A. (ed.). "Sequence A001748". 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.

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* 1980
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* 6174
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* 7744
* 7825
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* 8128
* 8192
* 9000
* 9855
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* 10,000
* 16,807
* 20,000
* 30,000
* 40,000
* 50,000
* 60,000
* 64,079
* 65,535
* 65,536
* 65,537
* 70,000
* 80,000
* 90,000

* 100,000
* 142,857
* 144,000
* 1,000,000
* 10,000,000
* 43,112,609
* 100,000,000
* 1,000,000,000
* 2,147,483,647
* 4,294,967,295
* 10,000,000,000
* 100,000,000,000

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