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Recognised as Number

1,684

  • Positive
  • Even
  • Composite
  • 4 digits

1,684 is an even 4-digit integer and a composite number. It has 6 divisors and a digital root of 1.

Number properties

ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value1,684
Digit count4
Digit sum19
Digit product192
Multiplicative persistence3times the digit product can be taken before one digit is left
Digital root1repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 421
Distinct prime factors22, 421
Number of divisors6
Sum of divisors σ(n)2,954
Aliquot sum1,270sum of the proper divisors
ClassificationDeficientthe aliquot sum is less than the number
Euler's totient φ(n)840integers below n that share no factor with it
Carmichael function λ(n)420the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 840
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 4, 421, 842, 1,6846 in total

Arithmetic

Previous number1,683
Next number1,685
Double3,368
Half842
Square2,835,856
Cube4,775,581,504
Square root41.036569057≈irrational, shown to 9 decimal places
Cube root11.897271224≈
Negation-1,684
Reciprocal0.0005938242≈

Representations

Decimal1,684
Binary1101001010011 bits
Octal3224
Hexadecimal694
Base 361AS
Roman numeralMDCLXXXIV
In wordsone thousand, six hundred and eighty-four
Ordinalone thousand, six hundred and eighty-fourth
Scientific notation1.684 × 10^3
Engineering notation1.684 × 10^3

In other bases

Ternary2022101base 3; the most digit-efficient integer base after e: 7 digits
Quinary23214base 5; one hand: 5 digits
Septenary4624base 7: 4 digits
Nonary2271base 9; each digit is two ternary digits: 4 digits
Duodecimalb84base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 3 digits
Vigesimal444base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal28:4base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternary1T10T101digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1101110010100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0000011010010100
Bit length11 bitsto write the magnitude
Set bits5the population count, or Hamming weight
Zero bits6within that length
Bit parityodd5 set bits, so odd; not the same as the number itself being even
Highest set bitbit 10worth 1,024
Lowest set bitbit 22 trailing zeros
Power of twoNo
Bytes206 94
Gray code10111011110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0000011010010100
32-bit00000000000000000000011010010100
64-bit0000000000000000000000000000000000000000000000000000011010010100
One's complement1111100101101011at 16 bits, every bit flipped
Bits reversed0010100101100000at 16 bits
Rotated left by 10000110100101000at 16 bits, wrapping
Shifted left by 1110100101000= 3,368, no wrap
Shifted right by 11101001010= 842, discarding the low bit
These bits as a double8.32006548 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,693+9
Previous prime1,669−15
Distance to nearest prime9
Nearest square below1,681
Nearest square above1,764

Powers & multiples

1,684 to the power 22,835,856
1,684 to the power 34,775,581,504
1,684 to the power 48,042,079,252,736
1,684 to the power 513,542,861,461,607,424
First ten multiples1,684, 3,368, 5,052, 6,736, 8,420, 10,104, 11,788, 13,472, 15,156, 16,840
Powers of twoBetween 2^10 (1,024) and 2^11 (2,048)

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 4
Divisible by 8No, remainder 4
Divisible by 9No, remainder 1
Divisible by 10No, remainder 4
Divisible by 11No, remainder 1
Divisible by 12No, remainder 4
Divisible by 100No, remainder 84

Collatz (3n + 1) trajectory

Steps to reach 142the total stopping time
Highest value reached1,684
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps1,684 → 842 → 421 → 1,264 → 632 → 316 → 158 → 79 → 238 → 119 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage168,400%
1,684% as a decimal16.84
1,684% of 1001,684
1,684% of 1,00016,840
As a fraction of 1001,684/100

Read another way

As seconds28 minutes and 4 seconds
As bytes1.645 KiB
As a year1684 AD
As a 24-bit colour#000694

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Neighbouring numbers

Nearby primes

Also reads as

1684 (year)

  • Leap year
  • 366 days
  • 17th century
  • Rat

1684 was a leap year of 366 days. It began on a Saturday and ended on a Sunday. Easter Sunday fell on 2 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
Century17th century
Decade1680s
Chinese zodiacRat
Easter Sunday2 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 as1656the most recent year whose calendar is identical, so a printed one could be reused
Calendar repeats in1724, 1752, 178040 years later, then again after that; the gap is 6, 11 or 28 years, broken by centuries that skip a leap year

Months of 1684

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 start-9,025,257,600
Unix timestamp at the end-8,993,635,201
Years from now342 years ago
Days from today125,170 days since 1 January

The number 1684

As a number1,684
In wordsone thousand, six hundred and eighty-four
Roman numeralsMDCLXXXIV

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Neighbouring years

Also reads as

#116688 (colour)

  • #116688
  • Cyan
  • Dark
  • Nearest: Steel blue

#116688 is a cyan with RGB values 17, 102, 136 and HSL 197°, 78%, 30%. It is a dark colour, so white text on it reaches 6.4:1 contrast (AA for normal text). The nearest named colour is Steel blue.

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Colour values

#116688#116688
HEX#116688
HEX (short)#168
RGBrgb(17, 102, 136)
RGB (0–1)0.0667, 0.4, 0.5333
RGB percentages6.7%, 40%, 53.3%
HSLhsl(197.1, 77.8%, 30%)
HSV / HSBhsv(197.1, 87.5%, 53.3%)
CMYK87.5%, 25%, 0%, 46.7%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer1,140,360
CSS custom property--colour: #116688;

Brightness & contrast

Relative luminance0.11399WCAG 2.x, 0 is black and 1 is white
Perceived brightness91.1 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 6.4:1
Contrast with white6.4:1WCAG normal text: AA
Contrast with black3.28:1WCAG normal text: Fail
Greyscale equivalent#565656
Inverted#EE9977

Colour vision & accessibility

Normal visionProtanopiaDeuteranopiaTritanopia
Protanopia#55658Ano red cones; affects about 1% of men; ΔE 15.3 from the original
Deuteranopia#455A87no green cones; the most common form, about 1% of men; ΔE 16.4 from the original
Tritanopia#006F72no blue cones; rare, and affects men and women equally; ΔE 21.5 from the original
Distinguishable without hueShifts in lightness toonever rely on hue alone to carry meaning
Contrast with white, large text6.4:1WCAG large text: AAA
Contrast with black, large text3.28:1WCAG large text: AA

Named colours

Steel blue · ΔE 15.6Slate grey · ΔE 21.4Light slate grey · ΔE 23Dark slate grey · ΔE 23.6Teal · ΔE 25.9Dim grey · ΔE 28.1
Nearest named CSS colourSteel blue (#4682B4)ΔE 15.57, a distinctly different colour
Hue familycyan
CSS keyword usableNo exact keyword

Colour harmonies

base+30°+90°+120°+180°+210°+240°+270°+330°
Complementary#883311
Analogous#11886E, #112B88
Triadic#881166, #668811
Split complementary#88112B, #886E11
Tetradic#6E1188, #883311, #2B8811

Tints, shades & saturation

+40%+30%+20%+10%base-10%-20%-30%-40%
Lighter +40%#77CCEE
Lighter +30%#4ABBE8
Lighter +20%#1CAAE3
Lighter +10%#1788B5
Darker −10%#0B445B
Darker −20%#06222D
Darker −30%#000000
Darker −40%#000000
More saturated +25%#006D99
Less saturated −25%#245E75

Channel breakdown

R17
G102
B136
Red17 (6.7%)
Green102 (40%)
Blue136 (53.3%)
Hue197.14°
Saturation (HSL)77.78%
Lightness30%
Dominant channelBlue
Hex per channelR 11 · G 66 · B 88

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Every value on this page was computed from “1684” by Nerdulator’s number engine. Nothing here was retrieved from a database of answers or written by a model.