# 34 (number)

34 is the natural number following 33 and preceding 35.

 List of numbers — Integers << 30 31 32 33 34 35 36 37 38 39 >>
Cardinal thirty-four
Ordinal34th (thirty-fourth)
Factorization[itex]2\cdot 17[itex]
Roman numeralXXXIV
Binary100010

## Mathematics

34 has four divisors, 1, 2, 17 and itself. Its neighbors, 33 and 35 also have four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has.

It is the ninth Fibonacci number and a companion Pell number.

This number is the magic constant of a 4 by 4 magic square:

[itex] \begin{bmatrix}

16 & 3 & 2 & 13 \\
5 & 10 & 11 & 8 \\
9 & 6 & 7 & 12 \\
4 & 15 & 14 & 1


\end{bmatrix} [itex]

This number is also the magic constant of n-Queens Problem for n = 4.

Thirty-four is a heptagonal number.

There is no answer to the equation φ(x) = 34, making 34 a nontotient. Nor is there an answer to the equation x - φ(x) = 34, making 34 a noncototient.

## In science

In astronomy,

Messier object M34, a magnitude 6.0 open cluster in the constellation Perseus
The New General Catalogue object (http://www.ngcic.org/) NGC 34, a peculiar galaxy in the constellation Cetus
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html) of the solar eclipse series which began on -1917 August 4 and ended on -384 February 9. The duration of Saros series 34 was 1532.5 years, and it contained 86 solar eclipses.
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html) of the lunar eclipse series which began on -1633 May 2 and ended on -335 June 19. The duration of Saros series 34 was 1298.1 years, and it contained 73 lunar eclipses.

## Other fields

Thirty-four is also:

es:Treinta y cuatro

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy
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