Recognised as Number
4,096
- Positive
- Even
- Composite
- Perfect square
- Perfect cube
- 4 digits
4,096 is an even 4-digit integer and a composite number. It has 13 divisors and a digital root of 1.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value4,096
Digit count4
Digit sum19
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root1repeated digit sum
PalindromicNoreads differently backwards
Perfect squareYes, 64²
Perfect cubeYes, 16³
Happy numberYessquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2^12
Distinct prime factors12
Number of divisors13
Sum of divisors σ(n)8,191
Aliquot sum4,095sum of the proper divisors
ClassificationDeficientthe aliquot sum is less than the number
Euler's totient φ(n)2,048integers below n that share no factor with it
Carmichael function λ(n)1,024the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 2,048
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, 4,09613 in total
Arithmetic
Previous number4,095
Next number4,097
Double8,192
Half2,048
Square16,777,216
Cube68,719,476,736
Square root64exact
Cube root16
Negation-4,096
Reciprocal0.0002441406≈
Representations
Decimal4,096
Binary100000000000013 bits
Octal10000
Hexadecimal1000
Base 3635S
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsfour thousand and ninety-six
Ordinalfour thousand and ninety-sixth
Scientific notation4.096 × 10^3
Engineering notation4.096 × 10^3
In other bases
Ternary12121201base 3; the most digit-efficient integer base after e: 8 digits
Quinary112341base 5; one hand: 6 digits
Septenary14641base 7: 5 digits
Nonary5551base 9; each digit is two ternary digits: 4 digits
Duodecimal2454base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimala4gbase 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal1:8:16base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternary1T0T0TT01digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1000000000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0001000000000000
Bit length13 bitsto write the magnitude
Set bits1the population count, or Hamming weight
Zero bits12within that length
Bit parityodd1 set bits, so odd; not the same as the number itself being even
Highest set bitbit 12worth 4,096
Lowest set bitbit 1212 trailing zeros
Power of twoYesexactly 2^12, a single set bit
Bytes210 00
Gray code1100000000000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit0001000000000000
32-bit00000000000000000001000000000000
64-bit0000000000000000000000000000000000000000000000000001000000000000
One's complement1110111111111111at 16 bits, every bit flipped
Bits reversed0000000000001000at 16 bits
Rotated left by 10010000000000000at 16 bits, wrapping
Shifted left by 110000000000000= 8,192, no wrap
Shifted right by 1100000000000= 2,048, discarding the low bit
These bits as a double2.02369289 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
4,096 to the power 216,777,216
4,096 to the power 368,719,476,736
4,096 to the power 4281,474,976,710,656
4,096 to the power 51,152,921,504,606,846,976
First ten multiples4,096, 8,192, 12,288, 16,384, 20,480, 24,576, 28,672, 32,768, 36,864, 40,960
Powers of twoExactly 2^12
Divisibility tests
Divisible by 2Yes
Divisible by 3No, remainder 1
Divisible by 4Yes
Divisible by 5No, remainder 1
Divisible by 6No, remainder 4
Divisible by 7No, remainder 1
Divisible by 8Yes
Divisible by 9No, remainder 1
Divisible by 10No, remainder 6
Divisible by 11No, remainder 4
Divisible by 12No, remainder 4
Divisible by 100No, remainder 96
Collatz (3n + 1) trajectory
Steps to reach 112the total stopping time
Highest value reached4,096
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps4,096 → 2,048 → 1,024 → 512 → 256 → 128 → 64 → 32 → 16 → 8 → …
Last steps… → 32 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage409,600%
4,096% as a decimal40.96
4,096% of 1004,096
4,096% of 1,00040,960
As a fraction of 1004,096/100
Read another way
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Derived from 4,096
Also reads as
4096 (year)
- Leap year
- 366 days
- 41st century
- Rat
4096 will be a leap year of 366 days. It begins on a Sunday and ends on a Monday. Easter Sunday falls on 25 March.
Structure of the year
Patterns forced by the calendar
Weekday counts52 of each, plus an extra Sunday and Monday366 days is 52 weeks and 2 days, and the remainder starts on the weekday 1 January falls on
Sundays53one of the extras
Mondays53one of the extras
Tuesdays52
Wednesdays52
Thursdays52
Fridays52
Saturdays52
Friday the 13th3 of them13 January, 13 April, 13 July
ISO weeks52an ordinary 52-week year
Same calendar as4068the most recent year whose calendar is identical, so a printed one could be reused
Calendar repeats in4108, 4136, 416412 years later, then again after that; the gap is 6, 11 or 28 years, broken by centuries that skip a leap year
Months of 4096
January31 days, starts Sunday
February29 days, starts Wednesday
September30 days, starts Saturday
October31 days, starts Monday
November30 days, starts Thursday
December31 days, starts Saturday
Time references
These values depend on today’s date and change daily.
Unix timestamp at the start67,090,118,400
Unix timestamp at the end67,121,740,799
Years from now2,070 years from now
Days from today755,797 days to 1 January
The number 4096
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Also reads as
#440099 (colour)
- #440099
- Violet
- Dark
- Nearest: Dark blue
#440099 is a violet with RGB values 68, 0, 153 and HSL 267°, 100%, 30%. It is a dark colour, so white text on it reaches 12.3:1 contrast (AAA for normal text). The nearest named colour is Dark blue.
Colour values
#440099#440099
HEX#440099
HEX (short)#409
RGBrgb(68, 0, 153)
RGB (0–1)0.2667, 0, 0.6
RGB percentages26.7%, 0%, 60%
HSLhsl(266.7, 100%, 30%)
HSV / HSBhsv(266.7, 100%, 60%)
CMYK55.6%, 100%, 0%, 40%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer4,456,601
CSS custom property--colour: #440099;
Brightness & contrast
Relative luminance0.03529WCAG 2.x, 0 is black and 1 is white
Perceived brightness63.6 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 12.31:1
Contrast with white12.31:1WCAG normal text: AAA
Contrast with black1.71:1WCAG normal text: Fail
Greyscale equivalent#1A1A1A
Inverted#BBFF66
Colour vision & accessibility
Distinguishable without hueShifts in lightness toonever rely on hue alone to carry meaning
Contrast with white, large text12.31:1WCAG large text: AAA
Contrast with black, large text1.71:1WCAG large text: Fail
Named colours
Hue familyviolet
CSS keyword usableNo exact keyword
Colour harmonies
Complementary#559900
Analogous#000899, #910099
Triadic#994400, #009944
Split complementary#999100, #089900
Tetradic#990008, #559900, #009991
Tints, shades & saturation
Channel breakdown
R68
G0
B153
Red68 (26.7%)
Green0 (0%)
Blue153 (60%)
Hue266.67°
Saturation (HSL)100%
Lightness30%
Dominant channelBlue
Hex per channelR 44 · G 00 · B 99
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