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
Roman numeral	XXXV
Binary	1000112
Ternary	10223
Quaternary	2034
Quinary	1205
Senary	556
Octal	438
Duodecimal	2B12
Hexadecimal	2316
Vigesimal	1F20
Base 36	Z36

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 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,^[2] a pentagonal number^[3] and a pentatope number.^[4]

35 is a highly cototient number, since there are more solutions to the equation x − φ(x) = 35 than there are for any other integers below it except 1.^[5]

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

Since the greatest prime factor of 35² + 1 = 1226 is 613, which is obviously more than 35 twice, 35 is a Størmer number.^[6]

35 is a discrete semiprime (or biprime) (5 × 7); the tenth, and the first with 5 as the lowest non-unitary factor. The aliquot sum of 35 is 13 this being the second composite number with such an aliquot sum; 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 discrete semiprime cluster is 85, 86, 87.

35 is the highest number one can count to on one's fingers using base 6.

35 is the number of quasigroups of order 4

In science

• The atomic number of bromine

Sports

• The jersey number 35 has been retired by several North American sports teams in honor of past playing greats or other key figures:
  • In Major League Baseball:
    • The Atlanta Braves, for Hall of Famer Phil Niekro.
    • The Chicago White Sox, for 2014 Hall of Fame inductee Frank Thomas.
    • The San Diego Padres, for Randy Jones.
  • In the NBA:
    • The Boston Celtics, for Reggie Lewis.
    • The Indiana Pacers, for Roger Brown.
    • The Utah Jazz, for Darrell Griffith.
  • In the NHL:
    • The Chicago Blackhawks, for Hall of Famer Tony Esposito.
  • In MotoGP, 35 is the rider number of British rider, Cal Crutchlow.

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 candidates for election to the United States or Irish Presidency.

References

1. "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
3. "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
4. "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.
5. "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
6. "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.