Recognised as Number
-10,004
- Negative
- Even
- 5 digits
-10,004 is an even 5-digit integer and the negative of 10,004. It has 12 divisors and a digital root of 5.
Number properties
ParityEvendivisible by 2
SignNegative
Absolute value10,004
Digit count5
Digit sum5
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root5repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 2^2 × 41 × 61
Distinct prime factors32, 41, 61
Number of divisors12
Sum of divisors σ(n)18,228
SquarefreeNohas a repeated prime factor
All divisors1, 2, 4, 41, 61, 82, 122, 164, 244, 2,501, 5,002, 10,00412 in total
Arithmetic
Representations
Decimal-10,004
Binary1001110001010014 bits
Octal23424
Hexadecimal2714
Base 367PW
In wordsminus ten thousand and four
Ordinalminus ten thousand and fourth
Scientific notation-1.0004 × 10^4
Engineering notation-10.004 × 10^3
In other bases
Ternary111201112base 3; the most digit-efficient integer base after e: 9 digits
Quinary310004base 5; one hand: 6 digits
Septenary41111base 7: 5 digits
Nonary14645base 9; each digit is two ternary digits: 5 digits
Duodecimal5958base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimal1504base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits
Sexagesimal2:46:44base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternaryT1111T1111digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary10100100111100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1101100011101100
Bit length14 bitsto write the magnitude
Set bits6the population count, or Hamming weight
Zero bits8within that length
Bit parityeven6 set bits, so even; not the same as the number itself being even
Highest set bitbit 13worth 8,192
Lowest set bitbit 22 trailing zeros
Power of twoNo
Bytes227 14
Gray code11010010011110n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1101100011101100two's complement
32-bit11111111111111111101100011101100two's complement
64-bit1111111111111111111111111111111111111111111111111101100011101100two's complement
One's complement0010011100010011at 16 bits, every bit flipped
Bits reversed0011011100011011at 16 bits
Rotated left by 11011000111011001at 16 bits, wrapping
Shifted left by 1-100111000101000= -20,008, no wrap
Shifted right by 1-1001110001010= -5,002, discarding the low bit
These bits as a double4.94263272 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-10,004 to the power 2100,080,016
-10,004 to the power 3-1,001,200,480,064
-10,004 to the power 410,016,009,602,560,256
-10,004 to the power 5-100,200,160,064,012,801,024
First ten multiples-10,004, -20,008, -30,012, -40,016, -50,020, -60,024, -70,028, -80,032, -90,036, -100,040
Powers of twoBetween 2^13 (8,192) and 2^14 (16,384)
Divisibility tests
Divisible by 2Yes
Divisible by 3No, remainder 2
Divisible by 4Yes
Divisible by 5No, remainder 4
Divisible by 6No, remainder 2
Divisible by 7No, remainder 1
Divisible by 8No, remainder 4
Divisible by 9No, remainder 5
Divisible by 10No, remainder 4
Divisible by 11No, remainder 5
Divisible by 12No, remainder 8
Divisible by 100No, remainder 4
As a percentage & fraction
As a percentage-1,000,400%
-10,004% as a decimal-100.04
-10,004% of 100-10,004
-10,004% of 1,000-100,040
As a fraction of 100-10,004/100
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