Recognised as Number
-37,137
- Negative
- Odd
- 5 digits
-37,137 is an odd 5-digit integer and the negative of 37,137. It has 4 divisors and a digital root of 3.
Number properties
ParityOddnot divisible by 2
SignNegative
Absolute value37,137
Digit count5
Digit sum21
Digit product441
Multiplicative persistence3times the digit product can be taken before one digit is left
Digital root3repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 3 × 12,379
Distinct prime factors23, 12,379
Number of divisors4
Sum of divisors σ(n)49,520
SquarefreeYesno repeated prime factor
All divisors1, 3, 12,379, 37,1374 in total
Arithmetic
Representations
Decimal-37,137
Binary100100010001000116 bits
Octal110421
Hexadecimal9111
Base 36SNL
In wordsminus thirty-seven thousand, one hundred and thirty-seven
Ordinalminus thirty-seven thousand, one hundred and thirty-seventh
Scientific notation-3.7137 × 10^4
Engineering notation-37.137 × 10^3
In other bases
Ternary1212221110base 3; the most digit-efficient integer base after e: 10 digits
Quinary2142022base 5; one hand: 7 digits
Septenary213162base 7: 6 digits
Nonary55843base 9; each digit is two ternary digits: 5 digits
Duodecimal195a9base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits
Vigesimal4cghbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits
Sexagesimal10:18:57base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternaryT101001TTT0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1011001100110011base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
11111111111111110110111011101111
Bit length16 bitsto write the magnitude
Set bits5the population count, or Hamming weight
Zero bits11within that length
Bit parityodd5 set bits, so odd; not the same as the number itself being odd
Highest set bitbit 15worth 32,768
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes291 11
Gray code1101100110011001n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit11111111111111110110111011101111two's complement
64-bit1111111111111111111111111111111111111111111111110110111011101111two's complement
One's complement00000000000000001001000100010000at 32 bits, every bit flipped
Bits reversed11110111011101101111111111111111at 32 bits
Rotated left by 111111111111111101101110111011111at 32 bits, wrapping
Shifted left by 1-10010001000100010= -74,274, no wrap
Shifted right by 1-100100010001001= -18,568, discarding the low bit
These bits as a double1.83481159 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-37,137 to the power 21,379,156,769
-37,137 to the power 3-51,217,744,930,353
-37,137 to the power 41,902,073,393,478,519,361
-37,137 to the power 5-70,637,299,613,611,773,509,457
First ten multiples-37,137, -74,274, -111,411, -148,548, -185,685, -222,822, -259,959, -297,096, -334,233, -371,370
Powers of twoBetween 2^15 (32,768) and 2^16 (65,536)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3Yes
Divisible by 4No, remainder 1
Divisible by 5No, remainder 2
Divisible by 6No, remainder 3
Divisible by 7No, remainder 2
Divisible by 8No, remainder 1
Divisible by 9No, remainder 3
Divisible by 10No, remainder 7
Divisible by 11No, remainder 1
Divisible by 12No, remainder 9
Divisible by 100No, remainder 37
As a percentage & fraction
As a percentage-3,713,700%
-37,137% as a decimal-371.37
-37,137% of 100-37,137
-37,137% of 1,000-371,370
As a fraction of 100-37,137/100
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