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Recognised as Number

2,000

  • Positive
  • Even
  • Composite
  • 4 digits

2,000 is an even 4-digit integer and a composite number. It has 20 divisors and a digital root of 2.

Number properties

ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value2,000
Digit count4
Digit sum2
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root2repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^4 × 5^3
Distinct prime factors22, 5
Number of divisors20
Sum of divisors σ(n)4,836
Aliquot sum2,836sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)800integers below n that share no factor with it
Carmichael function λ(n)100the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 800
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1,000, 2,00020 in total

Arithmetic

Previous number1,999
Next number2,001
Double4,000
Half1,000
Square4,000,000
Cube8,000,000,000
Square root44.72135955≈irrational, shown to 9 decimal places
Cube root12.599210499≈
Negation-2,000
Reciprocal0.0005≈

Representations

Decimal2,000
Binary1111101000011 bits
Octal3720
Hexadecimal7D0
Base 361JK
Roman numeralMM
In wordstwo thousand
Ordinaltwo thousandth
Scientific notation2 × 10^3
Engineering notation2 × 10^3

In other bases

Ternary2202002base 3; the most digit-efficient integer base after e — 7 digits
Quinary31000base 5; one hand — 5 digits
Septenary5555base 7 — 4 digits
Nonary2662base 9; each digit is two ternary digits — 4 digits
Duodecimal11a8base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves — 4 digits
Vigesimal500base 20; hands and feet, and the Mayan and Yoruba systems — 3 digits
Sexagesimal33:20base 60; Babylonian, and still how an hour and a circle are divided — 2 digits
Balanced ternary10T1T01Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1100011010000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0000011111010000
Bit length11 bitsto write the magnitude
Set bits6the population count, or Hamming weight
Zero bits5within that length
Bit parityeven6 set bits, so even; not the same as the number itself being even
Highest set bitbit 10worth 1,024
Lowest set bitbit 44 trailing zeros
Power of twoNo
Bytes207 d0
Gray code10000111000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0000011111010000
32-bit00000000000000000000011111010000
64-bit0000000000000000000000000000000000000000000000000000011111010000
One's complement1111100000101111at 16 bits, every bit flipped
Bits reversed0000101111100000at 16 bits
Rotated left by 10000111110100000at 16 bits, wrapping
Shifted left by 1111110100000= 4,000, no wrap
Shifted right by 11111101000= 1,000, discarding the low bit
These bits as a double9.88131292 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime2,003+3
Previous prime1,999−1
Distance to nearest prime1
Nearest square below1,936
Nearest square above2,025

Powers & multiples

2,000 to the power 24,000,000
2,000 to the power 38,000,000,000
2,000 to the power 416,000,000,000,000
2,000 to the power 532,000,000,000,000,000
First ten multiples2,000, 4,000, 6,000, 8,000, 10,000, 12,000, 14,000, 16,000, 18,000, 20,000
Powers of twoBetween 2^10 (1,024) and 2^11 (2,048)

Divisibility tests

Divisible by 2Yes
Divisible by 3No, remainder 2
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6No, remainder 2
Divisible by 7No, remainder 5
Divisible by 8Yes
Divisible by 9No, remainder 2
Divisible by 10Yes
Divisible by 11No, remainder 9
Divisible by 12No, remainder 8
Divisible by 100Yes

Collatz (3n + 1) trajectory

Steps to reach 1112the total stopping time
Highest value reached9,2324× the starting value
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps2,000 → 1,000 → 500 → 250 → 125 → 376 → 188 → 94 → 47 → 142 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage200,000%
2,000% as a decimal20
2,000% of 1002,000
2,000% of 1,00020,000
As a fraction of 1002,000/100

Read another way

As seconds33 minutes and 20 seconds
As bytes1.953 KiB
As a year2000 AD
As a 24-bit colour#0007D0

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Neighbouring numbers

Nearby primes

Also reads as

2000 (year)

  • Leap year
  • 366 days
  • 20th century
  • Dragon

2000 was a leap year of 366 days. It began on a Saturday and ended on a Sunday. Easter Sunday fell on 23 April.

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Structure of the year

Leap yearYesdivisible by 4, and by 400 if divisible by 100
Days in the year366
Days in February29
1 January fell on aSaturday
31 December fell on aSunday
Century20th century
Decade2000s
Chinese zodiacDragon
Easter Sunday23 April

Patterns forced by the calendar

Weekday counts52 of each, plus an extra Sunday and Saturday366 days is 52 weeks and 2 days, and the remainder starts on the weekday 1 January falls on
Sundays53one of the extras
Mondays52
Tuesdays52
Wednesdays52
Thursdays52
Fridays52
Saturdays53one of the extras
Friday the 13th1 of them13 October
ISO weeks52an ordinary 52-week year
Same calendar as1972the most recent year whose calendar is identical, so a printed one could be reused
Calendar repeats in2028, 2056, 208428 years later, then again after that — the gap is 6, 11 or 28 years, broken by centuries that skip a leap year

Months of 2000

January31 days, starts Saturday
February29 days, starts Tuesday
March31 days, starts Wednesday
April30 days, starts Saturday
May31 days, starts Monday
June30 days, starts Thursday
July31 days, starts Saturday
August31 days, starts Tuesday
September30 days, starts Friday
October31 days, starts Sunday
November30 days, starts Wednesday
December31 days, starts Friday

Time references

These values depend on today’s date and change daily.

Unix timestamp at the start946,684,800
Unix timestamp at the end978,307,199
Years from now26 years ago
Days from today9,751 days since 1 January

The number 2000

As a number2,000
In wordstwo thousand
Roman numeralsMM

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Neighbouring years

Also reads as

#220000 (colour)

  • #220000
  • Red
  • Dark
  • Nearest: Black

#220000 is a red with RGB values 34, 0, 0 and HSL 0°, 100%, 7%. It is a dark colour, so white text on it reaches 19.7:1 contrast (AAA for normal text). The nearest named colour is Black.

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Colour values

#220000#220000
HEX#220000
HEX (short)#200
RGBrgb(34, 0, 0)
RGB (0–1)0.1333, 0, 0
RGB percentages13.3%, 0%, 0%
HSLhsl(0, 100%, 6.7%)
HSV / HSBhsv(0, 100%, 13.3%)
CMYK0%, 100%, 100%, 86.7%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer2,228,224
CSS custom property--colour: #220000;

Brightness & contrast

Relative luminance0.0034WCAG 2.x, 0 is black and 1 is white
Perceived brightness18.6 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 19.66:1
Contrast with white19.66:1WCAG normal text: AAA
Contrast with black1.07:1WCAG normal text: Fail
Greyscale equivalent#070707
Inverted#DDFFFF

Colour vision & accessibility

Normal visionProtanopiaDeuteranopiaTritanopia
Protanopia#080600no red cones; affects about 1% of men; ΔE 14.4 from the original
Deuteranopia#120E00no green cones; the most common form, about 1% of men; ΔE 14.4 from the original
Tritanopia#270000no blue cones; rare, and affects men and women equally; ΔE 4 from the original
Distinguishable without hueYesnever rely on hue alone to carry meaning
Contrast with white, large text19.66:1WCAG large text: AAA
Contrast with black, large text1.07:1WCAG large text: Fail

Named colours

Black · ΔE 14.9Dark slate grey · ΔE 39Dim grey · ΔE 43.8Saddle brown · ΔE 51.5Gray · ΔE 52.6Maroon · ΔE 52.7
Nearest named CSS colourBlack (#000000)ΔE 14.93, a distinctly different colour
Hue familyred
CSS keyword usableNo exact keyword

Colour harmonies

base+30°+90°+120°+180°+210°+240°+270°+330°
Complementary#002222
Analogous#220011, #221100
Triadic#002200, #000022
Split complementary#002211, #001122
Tetradic#112200, #002222, #110022

Tints, shades & saturation

+40%+30%+20%+10%base-10%-20%-30%-40%
Lighter +40%#EE0000
Lighter +30%#BB0000
Lighter +20%#880000
Lighter +10%#550000
Darker −10%#000000
Darker −20%#000000
Darker −30%#000000
Darker −40%#000000
More saturated +25%#220000
Less saturated −25%#1E0404

Channel breakdown

R34
G0
B0
Red34 (13.3%)
Green0 (0%)
Blue0 (0%)
Hue0°
Saturation (HSL)100%
Lightness6.67%
Dominant channelRed
Hex per channelR 22 · G 00 · B 00

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Every value on this page was computed from “2000” by Nerdulator’s number engine. Nothing here was retrieved from a database of answers or written by a model.