Recognised as Number
-10,005
- Negative
- Odd
- 5 digits
-10,005 is an odd 5-digit integer and the negative of 10,005. It has 16 divisors and a digital root of 6.
Number properties
ParityOddnot divisible by 2
SignNegative
Absolute value10,005
Digit count5
Digit sum6
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root6repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 3 × 5 × 23 × 29
Distinct prime factors43, 5, 23, 29
Number of divisors16
Sum of divisors σ(n)17,280
SquarefreeYesno repeated prime factor
All divisors1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2,001, 3,335, 10,00516 in total
Arithmetic
Representations
Decimal-10,005
Binary1001110001010114 bits
Octal23425
Hexadecimal2715
Base 367PX
In wordsminus ten thousand and five
Ordinalminus ten thousand and fifth
Scientific notation-1.0005 × 10^4
Engineering notation-10.005 × 10^3
In other bases
Ternary111201120base 3; the most digit-efficient integer base after e: 9 digits
Quinary310010base 5; one hand: 6 digits
Septenary41112base 7: 5 digits
Nonary14646base 9; each digit is two ternary digits: 5 digits
Duodecimal5959base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimal1505base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits
Sexagesimal2:46:45base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternaryT1111T1110digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary10100100111111base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1101100011101011
Bit length14 bitsto write the magnitude
Set bits7the population count, or Hamming weight
Zero bits7within that length
Bit parityodd7 set bits, so odd; not the same as the number itself being odd
Highest set bitbit 13worth 8,192
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes227 15
Gray code11010010011111n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1101100011101011two's complement
32-bit11111111111111111101100011101011two's complement
64-bit1111111111111111111111111111111111111111111111111101100011101011two's complement
One's complement0010011100010100at 16 bits, every bit flipped
Bits reversed1101011100011011at 16 bits
Rotated left by 11011000111010111at 16 bits, wrapping
Shifted left by 1-100111000101010= -20,010, no wrap
Shifted right by 1-1001110001011= -5,002, discarding the low bit
These bits as a double4.94312679 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-10,005 to the power 2100,100,025
-10,005 to the power 3-1,001,500,750,125
-10,005 to the power 410,020,015,005,000,625
-10,005 to the power 5-100,250,250,125,031,253,125
First ten multiples-10,005, -20,010, -30,015, -40,020, -50,025, -60,030, -70,035, -80,040, -90,045, -100,050
Powers of twoBetween 2^13 (8,192) and 2^14 (16,384)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3Yes
Divisible by 4No, remainder 1
Divisible by 5Yes
Divisible by 6No, remainder 3
Divisible by 7No, remainder 2
Divisible by 8No, remainder 5
Divisible by 9No, remainder 6
Divisible by 10No, remainder 5
Divisible by 11No, remainder 6
Divisible by 12No, remainder 9
Divisible by 100No, remainder 5
As a percentage & fraction
As a percentage-1,000,500%
-10,005% as a decimal-100.05
-10,005% of 100-10,005
-10,005% of 1,000-100,050
As a fraction of 100-10,005/100
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