35 (number)

← 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.

In mathematics

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

35 is the 10th discrete semiprime (${\displaystyle 5\times 7}$)

as the lowest non-unitary factor, thus being the first of the form (5.q) where q is a higher prime.

35 has two

pair.

The aliquot sum of 35 is

.

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

• motion pictures
  .
• The minimum age of presidential candidates for election to the
  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