49 (number)

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This article is about the number. For the steamboat, see Forty-Nine (steamboat).
48 49 50
Cardinal forty-nine
Ordinal 49th
(forty-ninth)
Factorization 72
Divisors 1, 7, 49
Roman numeral XLIX
Binary 1100012
Ternary 12113
Quaternary 3014
Quinary 1445
Senary 1216
Octal 618
Duodecimal 4112
Hexadecimal 3116
Vigesimal 2920
Base 36 1D36

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

In mathematics[edit]

  • 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[edit]

The fraction 149 is a repeating decimal with a period of 42:

149 = 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[edit]

  • 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.[1][2]

In astronomy[edit]

In religion[edit]

In sports[edit]

See also 49er.

In music[edit]

See also: 49er

In other fields[edit]

Forty-nine is:

References[edit]

  1. ^ Hammel, E.F. (2000). "The taming of "49" — Big Science in little time. Recollections of Edward F. Hammel, pp. 2-9. In: Cooper N.G. Ed. (2000). Challenges in Plutonium Science". Los Alamos Science 26 (1): 2–9. 
  2. ^ Hecker, S.S. (2000). "Plutonium: an historical overview. In: Challenges in Plutonium Science". Los Alamos Science 26 (1): 1–2. 
  3. ^ Audio commentary by Sherman Aexie and Sean Axmaker on the DVD of The Exiles