# 49 (number)

 ← 48 49 50 →
Cardinal forty-nine
Ordinal 49th
(forty-ninth)
Factorization 72
Divisors 1, 7, 49
Greek numeral ΜΘ´
Roman numeral XLIX
Binary 1100012
Ternary 12113
Quaternary 3014
Quinary 1445
Senary 1216
Octal 618
Duodecimal 4112
Vigesimal 2920
Base 36 1D36

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

## In mathematics

Forty-nine is the square of seven

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).[1]

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

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

1/49 = 0.0204081632 6530612244 8979591836 7346938775 51 (42 digits repeat)

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.[2][3]

## In music

• "49 Bye-Byes", a song on the self-titled album Crosby Stills and Nash
• "Days of 49", a Bob Dylan song on the album Self Portrait
• 49:00... Of Your Time/Life is a one-track solo album by Paul Westerberg.
• In Blues music lore, it was at the junction of US Highway 49 and 61 in Clarksdale, Mississippi, that legendary bluesman Robert Johnson sold his soul to the devil in return for fame and success. In later years Howlin' Wolf immortalized the road in the song “Highway 49”, originally written by Big Joe Williams.[citation needed]

Forty-nine is:

## References

1. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. ^ 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" (PDF). Los Alamos Science. 26 (1): 2–9.
3. ^ Hecker, S.S. (2000). "Plutonium: an historical overview. In: Challenges in Plutonium Science". Los Alamos Science. 26 (1): 1–2.
4. ^ "Forty-nine dance". Encyclopedia Britannica. Retrieved May 25, 2018.