34 (number)

34 is the natural number following 33 and preceding 35.

Cardinal	thirty-four
Ordinal	34th (thirty-fourth)
Factorization
Roman numeral	XXXIV
Binary	100010
Hexadecimal	22

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:

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

• The atomic number of selenium

In astronomy,

Messier object M34, a magnitude 6.0 open cluster in the constellation Perseus

The New General Catalogue object NGC 34 , a peculiar galaxy in the constellation Cetus

The Saros number 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 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:

• The magic square puzzle in the 1970s 34 Skidoo.
• In the title of the 1947 movie Miracle on 34th Street, remade in 1994.
• The number of the French department Hérault.
• The code for international direct dial phone calls to Spain.
• Historical years: 34 A.D., 34 B.C., or 1934.