Recognised as Number
-2,001
- Negative
- Odd
- 4 digits
-2,001 is an odd 4-digit integer and the negative of 2,001. It has 8 divisors and a digital root of 3.
Number properties
ParityOddnot divisible by 2
SignNegative
Absolute value2,001
Digit count4
Digit sum3
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root3repeated digit sum
PalindromicNoreads differently backwards
Factors & divisors
Prime factorisation−1 × 3 × 23 × 29
Distinct prime factors33, 23, 29
Number of divisors8
Sum of divisors σ(n)2,880
SquarefreeYesno repeated prime factor
All divisors1, 3, 23, 29, 69, 87, 667, 2,0018 in total
Arithmetic
Representations
Decimal-2,001
Binary1111101000111 bits
Octal3721
Hexadecimal7D1
Base 361JL
In wordsminus two thousand and one
Ordinalminus two thousand and first
Scientific notation-2.001 × 10^3
Engineering notation-2.001 × 10^3
In other bases
Ternary2202010base 3; the most digit-efficient integer base after e: 7 digits
Quinary31001base 5; one hand: 5 digits
Septenary5556base 7: 4 digits
Nonary2663base 9; each digit is two ternary digits: 4 digits
Duodecimal11a9base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimal501base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal33:21base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternaryT01T10T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary100001110011base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
1111100000101111
Bit length11 bitsto write the magnitude
Set bits7the population count, or Hamming weight
Zero bits4within that length
Bit parityodd7 set bits, so odd; not the same as the number itself being odd
Highest set bitbit 10worth 1,024
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes207 d1
Gray code10000111001n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit1111100000101111two's complement
32-bit11111111111111111111100000101111two's complement
64-bit1111111111111111111111111111111111111111111111111111100000101111two's complement
One's complement0000011111010000at 16 bits, every bit flipped
Bits reversed1111010000011111at 16 bits
Rotated left by 11111000001011111at 16 bits, wrapping
Shifted left by 1-111110100010= -4,002, no wrap
Shifted right by 1-1111101001= -1,000, discarding the low bit
These bits as a double9.88625357 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Powers & multiples
-2,001 to the power 24,004,001
-2,001 to the power 3-8,012,006,001
-2,001 to the power 416,032,024,008,001
-2,001 to the power 5-32,080,080,040,010,001
First ten multiples-2,001, -4,002, -6,003, -8,004, -10,005, -12,006, -14,007, -16,008, -18,009, -20,010
Powers of twoBetween 2^10 (1,024) and 2^11 (2,048)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3Yes
Divisible by 4No, remainder 1
Divisible by 5No, remainder 1
Divisible by 6No, remainder 3
Divisible by 7No, remainder 6
Divisible by 8No, remainder 1
Divisible by 9No, remainder 3
Divisible by 10No, remainder 1
Divisible by 11No, remainder 10
Divisible by 12No, remainder 9
Divisible by 100No, remainder 1
As a percentage & fraction
As a percentage-200,100%
-2,001% as a decimal-20.01
-2,001% of 100-2,001
-2,001% of 1,000-20,010
As a fraction of 100-2,001/100
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