Recognised as Number
2,016
- Positive
- Even
- Composite
- 4 digits
2,016 is an even 4-digit integer and a composite number. It has 36 divisors and a digital root of 9.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value2,016
Digit count4
Digit sum9
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root9repeated digit sum
PalindromicNoreads differently backwards
Triangular numberYes, the 63rd triangular number
Happy numberNosquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^5 × 3^2 × 7
Distinct prime factors32, 3, 7
Number of divisors36
Sum of divisors σ(n)6,552
Aliquot sum4,536sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)576integers below n that share no factor with it
Carmichael function λ(n)24the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 576
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1,008, 2,01636 in total
Arithmetic
Representations
Decimal2,016
Binary1111110000011 bits
Octal3740
Hexadecimal7E0
Base 361K0
Roman numeralMMXVI
In wordstwo thousand and sixteen
Ordinaltwo thousand and sixteenth
Scientific notation2.016 × 10^3
Engineering notation2.016 × 10^3
In other bases
Ternary2202200base 3; the most digit-efficient integer base after e: 7 digits
Quinary31031base 5; one hand: 5 digits
Septenary5610base 7: 4 digits
Nonary2680base 9; each digit is two ternary digits: 4 digits
Duodecimal1200base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimal50gbase 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal33:36base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternary10T10T00digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1100000100000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0000011111100000
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 55 trailing zeros
Power of twoNo
Bytes207 e0
Gray code10000010000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit0000011111100000
32-bit00000000000000000000011111100000
64-bit0000000000000000000000000000000000000000000000000000011111100000
One's complement1111100000011111at 16 bits, every bit flipped
Bits reversed0000011111100000at 16 bits
Rotated left by 10000111111000000at 16 bits, wrapping
Shifted left by 1111111000000= 4,032, no wrap
Shifted right by 11111110000= 1,008, discarding the low bit
These bits as a double9.96036342 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
2,016 to the power 24,064,256
2,016 to the power 38,193,540,096
2,016 to the power 416,518,176,833,536
2,016 to the power 533,300,644,496,408,576
First ten multiples2,016, 4,032, 6,048, 8,064, 10,080, 12,096, 14,112, 16,128, 18,144, 20,160
Powers of twoBetween 2^10 (1,024) and 2^11 (2,048)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5No, remainder 1
Divisible by 6Yes
Divisible by 7Yes
Divisible by 8Yes
Divisible by 9Yes
Divisible by 10No, remainder 6
Divisible by 11No, remainder 3
Divisible by 12Yes
Divisible by 100No, remainder 16
Collatz (3n + 1) trajectory
Steps to reach 1112the total stopping time
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps2,016 → 1,008 → 504 → 252 → 126 → 63 → 190 → 95 → 286 → 143 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage201,600%
2,016% as a decimal20.16
2,016% of 1002,016
2,016% of 1,00020,160
As a fraction of 1002,016/100
Read another way
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Derived from 2,016
Also reads as
2016 (year)
- Leap year
- 366 days
- 21st century
- Monkey
2016 was a leap year of 366 days. It began on a Friday and ended on a Saturday. Easter Sunday fell on 27 March.
Structure of the year
Patterns forced by the calendar
Weekday counts52 of each, plus an extra Friday and Saturday366 days is 52 weeks and 2 days, and the remainder starts on the weekday 1 January falls on
Sundays52
Mondays52
Tuesdays52
Wednesdays52
Thursdays52
Fridays53one of the extras
Saturdays53one of the extras
Friday the 13th1 of them13 May
ISO weeks52an ordinary 52-week year
Same calendar as1988the most recent year whose calendar is identical, so a printed one could be reused
Calendar repeats in2044, 2072, 211228 years later, then again after that; the gap is 6, 11 or 28 years, broken by centuries that skip a leap year
Months of 2016
January31 days, starts Friday
February29 days, starts Monday
August31 days, starts Monday
September30 days, starts Thursday
October31 days, starts Saturday
November30 days, starts Tuesday
December31 days, starts Thursday
Time references
These values depend on today’s date and change daily.
Unix timestamp at the start1,451,606,400
Unix timestamp at the end1,483,228,799
Years from now10 years ago
Days from today3,916 days since 1 January
The number 2016
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Also reads as
#220011 (colour)
- #220011
- Red
- Dark
- Nearest: Black
#220011 is a red with RGB values 34, 0, 17 and HSL 330°, 100%, 7%. It is a dark colour, so white text on it reaches 19.5:1 contrast (AAA for normal text). The nearest named colour is Black.
Colour values
#220011#220011
HEX#220011
HEX (short)#201
RGBrgb(34, 0, 17)
RGB (0–1)0.1333, 0, 0.0667
RGB percentages13.3%, 0%, 6.7%
HSLhsl(330, 100%, 6.7%)
HSV / HSBhsv(330, 100%, 13.3%)
CMYK0%, 100%, 50%, 86.7%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer2,228,241
CSS custom property--colour: #220011;
Brightness & contrast
Relative luminance0.00381WCAG 2.x, 0 is black and 1 is white
Perceived brightness19.5 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 19.51:1
Contrast with white19.51:1WCAG normal text: AAA
Contrast with black1.08:1WCAG normal text: Fail
Greyscale equivalent#080808
Inverted#DDFFEE
Colour vision & accessibility
Distinguishable without hueYesnever rely on hue alone to carry meaning
Contrast with white, large text19.51:1WCAG large text: AAA
Contrast with black, large text1.08:1WCAG large text: Fail
Named colours
Hue familyred
CSS keyword usableNo exact keyword
Colour harmonies
Complementary#002211
Analogous#220022, #220000
Triadic#112200, #001122
Split complementary#002200, #002222
Tetradic#222200, #002211, #000022
Tints, shades & saturation
Channel breakdown
R34
G0
B17
Red34 (13.3%)
Green0 (0%)
Blue17 (6.7%)
Hue330°
Saturation (HSL)100%
Lightness6.67%
Dominant channelRed
Hex per channelR 22 · G 00 · B 11
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Harmonies
Similar named colours
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