# 49 (number)

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

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

## In mathematics

Forty-nine is the square of the prime number seven and hence the fourth non-unitary square prime of the form p2

49 has an aliquot sum of 8; itself a prime power, and hence an aliquot sequence of two composite members (49, 8, 7,1,0).

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

The smallest triple of three squares in arithmetic succession is (1,25,49), and the second smallest is (49,169,289).

49 is the smallest discriminant of a totally real cubic field.[2]

49 and 94 are the only numbers below 100 whose all permutations are composites but they are not multiples of 3, repdigits or numbers which only have digits 0, 2, 4, 5, 6 and 8, even excluding the trivial one digit terms.

49 = 7^2 and 94 = 2 * 47

The number of prime knots with 9 crossings is 49.[3]

### 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 positive integers less than 49 and coprime to 49. (42 is the period.) 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:

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

## 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.[4][5]

Forty-nine is: