35 (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
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

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

In science

• The atomic number of bromine

In other fields

• 35 mm film is the basic film gauge most commonly used for both analog photography and motion pictures.
• The minimum age of presidential candidates for election to the United States, Ireland, Poland, Russia, Trinidad and Tobago, and Uruguay.
• For Social Security in the United States, the 35 highest years of earnings are used to calculate retirement benefits.

See also

• List of highways numbered 35

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.). "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.