Recognised as Number
8,040
- Positive
- Even
- Composite
- 4 digits
8,040 is an even 4-digit integer and a composite number. It has 32 divisors and a digital root of 3.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value8,040
Digit count4
Digit sum12
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
Happy numberNosquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^3 × 3 × 5 × 67
Distinct prime factors42, 3, 5, 67
Number of divisors32
Sum of divisors σ(n)24,480
Aliquot sum16,440sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)2,112integers below n that share no factor with it
Carmichael function λ(n)132the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 2,112
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 67, 120, 134, 201, 268, 335, 402, 536, 670, 804, 1,005, 1,340, 1,608, 2,010, 2,680, 4,020, 8,04032 in total
Arithmetic
Previous number8,039
Next number8,041
Double16,080
Half4,020
Square64,641,600
Cube519,718,464,000
Square root89.666047086≈irrational, shown to 9 decimal places
Cube root20.033277932≈
Negation-8,040
Reciprocal0.0001243781≈
Representations
Decimal8,040
Binary111110110100013 bits
Octal17550
Hexadecimal1F68
Base 3667C
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordseight thousand and forty
Ordinaleight thousand and fortieth
Scientific notation8.04 × 10^3
Engineering notation8.04 × 10^3
In other bases
Ternary102000210base 3; the most digit-efficient integer base after e: 9 digits
Quinary224130base 5; one hand: 6 digits
Septenary32304base 7: 5 digits
Nonary12023base 9; each digit is two ternary digits: 5 digits
Duodecimal47a0base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimal1020base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits
Sexagesimal2:14:0base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternary11T001T10digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary110000010111000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0001111101101000
Bit length13 bitsto write the magnitude
Set bits8the population count, or Hamming weight
Zero bits5within that length
Bit parityeven8 set bits, so even; not the same as the number itself being even
Highest set bitbit 12worth 4,096
Lowest set bitbit 33 trailing zeros
Power of twoNo
Bytes21f 68
Gray code1000011011100n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit0001111101101000
32-bit00000000000000000001111101101000
64-bit0000000000000000000000000000000000000000000000000001111101101000
One's complement1110000010010111at 16 bits, every bit flipped
Bits reversed0001011011111000at 16 bits
Rotated left by 10011111011010000at 16 bits, wrapping
Shifted left by 111111011010000= 16,080, no wrap
Shifted right by 1111110110100= 4,020, discarding the low bit
These bits as a double3.97228779 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
8,040 to the power 264,641,600
8,040 to the power 3519,718,464,000
8,040 to the power 44,178,536,450,560,000
8,040 to the power 533,595,433,062,502,400,000
First ten multiples8,040, 16,080, 24,120, 32,160, 40,200, 48,240, 56,280, 64,320, 72,360, 80,400
Powers of twoBetween 2^12 (4,096) and 2^13 (8,192)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6Yes
Divisible by 7No, remainder 4
Divisible by 8Yes
Divisible by 9No, remainder 3
Divisible by 10Yes
Divisible by 11No, remainder 10
Divisible by 12Yes
Divisible by 100No, remainder 40
Collatz (3n + 1) trajectory
Steps to reach 170the total stopping time
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps8,040 → 4,020 → 2,010 → 1,005 → 3,016 → 1,508 → 754 → 377 → 1,132 → 566 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage804,000%
8,040% as a decimal80.4
8,040% of 1008,040
8,040% of 1,00080,400
As a fraction of 1008,040/100
Read another way
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Derived from 8,040
Also reads as
8040 (year)
- Leap year
- 366 days
- 81st century
- Monkey
8040 will be a leap year of 366 days. It begins on a Sunday and ends on a Monday. Easter Sunday falls on 8 April.
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 as8012the most recent year whose calendar is identical, so a printed one could be reused
Calendar repeats in8068, 8096, 810828 years later, then again after that; the gap is 6, 11 or 28 years, broken by centuries that skip a leap year
Months of 8040
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 start191,550,700,800
Unix timestamp at the end191,582,323,199
Years from now6,014 years from now
Days from today2,196,313 days to 1 January
The number 8040
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Also reads as
#880044 (colour)
- #880044
- Red
- Dark
- Nearest: Medium violet red
#880044 is a red with RGB values 136, 0, 68 and HSL 330°, 100%, 27%. It is a dark colour, so white text on it reaches 9.9:1 contrast (AAA for normal text). The nearest named colour is Medium violet red.
Colour values
#880044#880044
HEX#880044
HEX (short)#804
RGBrgb(136, 0, 68)
RGB (0–1)0.5333, 0, 0.2667
RGB percentages53.3%, 0%, 26.7%
HSLhsl(330, 100%, 26.7%)
HSV / HSBhsv(330, 100%, 53.3%)
CMYK0%, 100%, 50%, 46.7%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer8,912,964
CSS custom property--colour: #880044;
Brightness & contrast
Relative luminance0.05652WCAG 2.x, 0 is black and 1 is white
Perceived brightness77.8 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 9.86:1
Contrast with white9.86:1WCAG normal text: AAA
Contrast with black2.13:1WCAG normal text: Fail
Greyscale equivalent#222222
Inverted#77FFBB
Colour vision & accessibility
Distinguishable without hueShifts in lightness toonever rely on hue alone to carry meaning
Contrast with white, large text9.86:1WCAG large text: AAA
Contrast with black, large text2.13:1WCAG large text: Fail
Named colours
Hue familyred
CSS keyword usableNo exact keyword
Colour harmonies
Complementary#008844
Analogous#880088, #880000
Triadic#448800, #004488
Split complementary#008800, #008888
Tetradic#888800, #008844, #000088
Tints, shades & saturation
Channel breakdown
R136
G0
B68
Red136 (53.3%)
Green0 (0%)
Blue68 (26.7%)
Hue330°
Saturation (HSL)100%
Lightness26.67%
Dominant channelRed
Hex per channelR 88 · G 00 · B 44
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Harmonies
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