49 (number)

This page is about the number. For the steamboat see Forty-Nine (steamboat)

← 48 49 50 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-nine
Ordinal	th
Factorization	$7^{2}$
Divisors	1, 7, 49
Greek numeral	ΜΘ´
Roman numeral	XLIX
Binary	1100012
Ternary	12113
Senary	1216
Octal	618
Duodecimal	4112
Hexadecimal	3116

49 (forty-nine) is the natural number following 48 and preceding 50.

In mathematics

• Forty-nine is the square of seven and is therefore the fourth squared prime number.

The aliquot sum of forty-nine is 8. and this number has an aliquot sequence of (8, 7, 1, 0 ).

49 is the 8th composite number in the 7-aliquot tree.

The sum of the digits of the square of 49 (2401) is the square root of 49.

49 is the first square where the digits are squares. In this case 4 and 9 are squares.

It appears in the Padovan sequence, preceded by the terms 21, 28, 37 (it is the sum of the first two of these).

Along with the number that immediately derives from it, 77, the only number under 3 digits not having its home prime known (as of late 2010).

Reciprocal

See also: Repeating decimal

The fraction 1⁄49 is a repeating decimal with a period of 42:

1⁄49 = 0.0204081632 6530612244 8979591836 7346938775 51 (42 repeating digits)

There are 42 (note that this number is the period) positive integers that are less than 49 and coprime to 49. Multiplying 020408163265306122448979591836734693877551 by each of these integers results in a cyclic permutation of the original number:

• 020408163265306122448979591836734693877551 × 2 = 040816326530612244897959183673469387755102
• 020408163265306122448979591836734693877551 × 3 = 061224489795918367346938775510204081632653
• 020408163265306122448979591836734693877551 × 4 = 081632653061224489795918367346938775510204
• ...

The repeating number can be obtained from 02 and repetition of doubles placed at two places to the right:

02
  04
    08
      16
        32
          64
           128
             256
               512
                1024
                  2048
+                   ...
----------------------
020408163265306122448979591836734693877551...0204081632...

In chemistry

• The atomic number of indium.
• During the Manhattan Project, plutonium was also often referred to, simply, as "49". Number 4 was for the last digit in 94 (atomic number of plutonium) and 9 for the last digit in Pu-239, the weapon-grade fissile isotope used in nuclear bombs.

In astronomy

• Messier object M49, a magnitude 10.0 galaxy in the constellation Virgo.
• The New General Catalogue object NGC 49, a spiral galaxy in the constellation Cetus.
• The Saros number of the solar eclipse series which began on -1248 February 22 and ended on 32 March. The duration of Saros series 49 was 1280.1 years, and it contained 72 solar eclipses.
• The Saros number of the lunar eclipse series which began on -1217 June 21 and ended on 81 August. The duration of Saros series 49 was 1298.1 years, and it contained 73 lunar eclipses.

In religion

• On the Hebrew calendar, the number of days of the Counting of the Omer
• The number of days and night Siddhartha Gautama spent meditating as a holy man
• Surely We have created everything with fate. (Al-Qamar Surah, 49)

In sports

See also 49er.

• 49er, the moniker of one who participated in the 1849 California Gold Rush, as well as the NFL's San Francisco 49ers.
• Houston Astros Larry Dierker's retired uniform #49.
• New York Yankees Ron Guidry’s retired uniform #49.
• Arsenal had a 49 game unbeaten run between May 2003 to October 2004 until they lost to Manchester United which is a national record in English football .

In music

See also: 49er

• Featured in the song title "49 Bye-Byes" in Crosby Stills and Nash's self-titled album
• "Days of 49", a Bob Dylan song
• 49:00... Of Your Time/Life is a one-track solo album by Paul Westerberg.

In other fields

Forty-nine is:

• HP-49 series is a Hewlett Packard calculator
• I-49 is the designation for a US interstate highway, currently open only in the state of Louisiana, but planned to extend into Arkansas and Missouri, eventually connecting Kansas City and New Orleans
• The code for international direct dial phone calls to Germany
• In the title of Thomas Pynchon's novel The Crying of Lot 49
• In the title of the movie Ladder 49
• In the title of the movie 49 Up
• A 49 is a term used to describe a party after a powwow or any gathering of American Indians, held by the participants. It also refers to a particular type of song that is sung on such occasions. A 49 is typically held in an isolated place and features drumming and singing.
• 49th State of the USA: Alaska
• 49th parallel between Canada and the USA
• Ernest Hemingway collection: The Fifth Column and The First Forty-Nine Stories
• Japanese GS1 country code
• The number of the French department Maine-et-Loire

Historical years

• 49 A.D., 49 B.C., 1949, 2049, etc.