# 49 (number)

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

 ← 48 49 50 →
Cardinalforty-nine
Ordinal49th
(forty-ninth)
Factorization72
Divisors1, 7, 49
Greek numeralΜΘ´
Roman numeralXLIX
Binary1100012
Ternary12113
Senary1216
Octal618
Duodecimal4112

## In mathematics

Forty-nine is the square of seven.

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 100 not having its home prime known (as of 2016).

### Decimal representation

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.

#### 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...


because 149 satisfies:

$x={\frac {1}{50}}+{\frac {2x}{100}}={\frac {1}{50}}(1+x)\,.$

## 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.

Forty-nine is: