Recognised as Number
1,024
- Positive
- Even
- Composite
- Perfect square
- 4 digits
1,024 is an even 4-digit integer and a composite number. It has 11 divisors and a digital root of 7.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value1,024
Digit count4
Digit sum7
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root7repeated digit sum
PalindromicNoreads differently backwards
Perfect squareYes, 32²
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2^10
Distinct prime factors12
Number of divisors11
Sum of divisors σ(n)2,047
Aliquot sum1,023sum of the proper divisors
ClassificationDeficientthe aliquot sum is less than the number
Euler's totient φ(n)512integers below n that share no factor with it
Carmichael function λ(n)256the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 512
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, 1,02411 in total
Arithmetic
Representations
Decimal1,024
Binary1000000000011 bits
Octal2000
Hexadecimal400
Base 36SG
Roman numeralMXXIV
In wordsone thousand and twenty-four
Ordinalone thousand and twenty-fourth
Scientific notation1.024 × 10^3
Engineering notation1.024 × 10^3
In other bases
Ternary1101221base 3; the most digit-efficient integer base after e: 7 digits
Quinary13044base 5; one hand: 5 digits
Septenary2662base 7: 4 digits
Nonary1357base 9; each digit is two ternary digits: 4 digits
Duodecimal714base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 3 digits
Vigesimal2b4base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal17:4base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternary111T0T1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary10000000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0000010000000000
Bit length11 bitsto write the magnitude
Set bits1the population count, or Hamming weight
Zero bits10within that length
Bit parityodd1 set bits, so odd; not the same as the number itself being even
Highest set bitbit 10worth 1,024
Lowest set bitbit 1010 trailing zeros
Power of twoYesexactly 2^10, a single set bit
Bytes204 00
Gray code11000000000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit0000010000000000
32-bit00000000000000000000010000000000
64-bit0000000000000000000000000000000000000000000000000000010000000000
One's complement1111101111111111at 16 bits, every bit flipped
Bits reversed0000000000100000at 16 bits
Rotated left by 10000100000000000at 16 bits, wrapping
Shifted left by 1100000000000= 2,048, no wrap
Shifted right by 11000000000= 512, discarding the low bit
These bits as a double5.05923221 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
1,024 to the power 21,048,576
1,024 to the power 31,073,741,824
1,024 to the power 41,099,511,627,776
1,024 to the power 51,125,899,906,842,624
First ten multiples1,024, 2,048, 3,072, 4,096, 5,120, 6,144, 7,168, 8,192, 9,216, 10,240
Powers of twoExactly 2^10
Divisibility tests
Divisible by 2Yes
Divisible by 3No, remainder 1
Divisible by 4Yes
Divisible by 5No, remainder 4
Divisible by 6No, remainder 4
Divisible by 7No, remainder 2
Divisible by 8Yes
Divisible by 9No, remainder 7
Divisible by 10No, remainder 4
Divisible by 11No, remainder 1
Divisible by 12No, remainder 4
Divisible by 100No, remainder 24
Collatz (3n + 1) trajectory
Steps to reach 110the total stopping time
Highest value reached1,024
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps1,024 → 512 → 256 → 128 → 64 → 32 → 16 → 8 → 4 → 2 → …
Last steps… → 32 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage102,400%
1,024% as a decimal10.24
1,024% of 1001,024
1,024% of 1,00010,240
As a fraction of 1001,024/100
Read another way
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Derived from 1,024
Also reads as
1024 (year)
- Leap year
- 366 days
- 11th century
- Rat
- 53 ISO weeks
1024 was a leap year of 366 days. It began on a Thursday and ended on a Friday. Easter Sunday fell on 4 April.
Structure of the year
Patterns forced by the calendar
Weekday counts52 of each, plus an extra Thursday and Friday366 days is 52 weeks and 2 days, and the remainder starts on the weekday 1 January falls on
Sundays52
Mondays52
Tuesdays52
Wednesdays52
Thursdays53one of the extras
Fridays53one of the extras
Saturdays52
Friday the 13th2 of them13 February, 13 August
ISO weeks53a long year: 1 January is a Thursday, or a Wednesday in a leap year, so a week 53 exists
Same calendar as984the most recent year whose calendar is identical, so a printed one could be reused
Calendar repeats in1052, 1080, 112028 years later, then again after that; the gap is 6, 11 or 28 years, broken by centuries that skip a leap year
Months of 1024
January31 days, starts Thursday
February29 days, starts Sunday
August31 days, starts Sunday
September30 days, starts Wednesday
October31 days, starts Friday
November30 days, starts Monday
December31 days, starts Wednesday
Time references
These values depend on today’s date and change daily.
Unix timestamp at the start-29,852,928,000
Unix timestamp at the end-29,821,305,601
Years from now1,002 years ago
Days from today366,271 days since 1 January
The number 1024
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Also reads as
#110022 (colour)
- #110022
- Violet
- Dark
- Nearest: Black
#110022 is a violet with RGB values 17, 0, 34 and HSL 270°, 100%, 7%. It is a dark colour, so white text on it reaches 20.1:1 contrast (AAA for normal text). The nearest named colour is Black.
Colour values
#110022#110022
HEX#110022
HEX (short)#102
RGBrgb(17, 0, 34)
RGB (0–1)0.0667, 0, 0.1333
RGB percentages6.7%, 0%, 13.3%
HSLhsl(270, 100%, 6.7%)
HSV / HSBhsv(270, 100%, 13.3%)
CMYK50%, 100%, 0%, 86.7%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer1,114,146
CSS custom property--colour: #110022;
Brightness & contrast
Relative luminance0.00235WCAG 2.x, 0 is black and 1 is white
Perceived brightness14.8 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 20.06:1
Contrast with white20.06:1WCAG normal text: AAA
Contrast with black1.05:1WCAG normal text: Fail
Greyscale equivalent#060606
Inverted#EEFFDD
Colour vision & accessibility
Distinguishable without hueYesnever rely on hue alone to carry meaning
Contrast with white, large text20.06:1WCAG large text: AAA
Contrast with black, large text1.05:1WCAG large text: Fail
Named colours
Hue familyviolet
CSS keyword usableNo exact keyword
Colour harmonies
Complementary#112200
Analogous#000022, #220022
Triadic#221100, #002211
Split complementary#222200, #002200
Tetradic#220000, #112200, #002222
Tints, shades & saturation
Channel breakdown
R17
G0
B34
Red17 (6.7%)
Green0 (0%)
Blue34 (13.3%)
Hue270°
Saturation (HSL)100%
Lightness6.67%
Dominant channelBlue
Hex per channelR 11 · G 00 · B 22
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Harmonies
Similar named colours
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