35 (thirty-five) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
34 and preceding
36.
In mathematics
35 is the sum of the first five
triangular numbers, making it a
tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular ...
.
35 is the 10th discrete
semiprime (
) 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 factor
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
s, (
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
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.
Def ...
of only one composite number (35,
13,
1,0) to the Prime in the
13-aliquot tree. 35 is the second
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...
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.
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, a
centered tetrahedral number, a
pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular number, triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotational ...
, and a
pentatope number.
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.
There are 35 free
hexominoes, the
polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling.
Polyominoes have been used in popu ...
es made from six squares.
Since the greatest prime factor of
is 613, which is more than 35 twice, 35 is a
Størmer number.
35 is the highest number one can count to on one's fingers using
senary
A senary () numeral system (also known as base-6, heximal, or seximal) has 6, six as its radix, base. It has been adopted independently by a small number of cultures. Like the decimal base 10, the base is a semiprime, though it is unique as the p ...
.
35 is the number of quasigroups of order 4.
35 is the smallest
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...
of the form
, where is a non-negative integer.
References
{{Integers, zero
Integers