Recognised as Number
4,137
- Positive
- Odd
- Composite
- 4 digits
4,137 is an odd 4-digit integer and a composite number. It has 8 divisors and a digital root of 6.
Number properties
ParityOddnot divisible by 2
SignPositive
PrimalityComposite
Absolute value4,137
Digit count4
Digit sum15
Digit product84
Multiplicative persistence3times the digit product can be taken before one digit is left
Digital root6repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation3 × 7 × 197
Distinct prime factors33, 7, 197
Number of divisors8
Sum of divisors σ(n)6,336
Aliquot sum2,199sum of the proper divisors
ClassificationDeficientthe aliquot sum is less than the number
Euler's totient φ(n)2,352integers below n that share no factor with it
Carmichael function λ(n)588the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 2,352
Möbius function μ(n)−13 distinct prime factors, an odd number of them
SquarefreeYesno repeated prime factor
All divisors1, 3, 7, 21, 197, 591, 1,379, 4,1378 in total
Arithmetic
Previous number4,136
Next number4,138
Double8,274
Half2,068.5
Square17,114,769
Cube70,803,799,353
Square root64.319514924≈irrational, shown to 9 decimal places
Cube root16.053208275≈
Negation-4,137
Reciprocal0.0002417211≈
Representations
Decimal4,137
Binary100000010100113 bits
Octal10051
Hexadecimal1029
Base 3636X
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsfour thousand, one hundred and thirty-seven
Ordinalfour thousand, one hundred and thirty-seventh
Scientific notation4.137 × 10^3
Engineering notation4.137 × 10^3
In other bases
Ternary12200020base 3; the most digit-efficient integer base after e: 8 digits
Quinary113022base 5; one hand: 6 digits
Septenary15030base 7: 5 digits
Nonary5606base 9; each digit is two ternary digits: 4 digits
Duodecimal2489base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimala6hbase 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal1:8:57base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternary1T0T001T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1000001111001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0001000000101001
Bit length13 bitsto write the magnitude
Set bits4the population count, or Hamming weight
Zero bits9within that length
Bit parityeven4 set bits, so even; not the same as the number itself being odd
Highest set bitbit 12worth 4,096
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes210 29
Gray code1100000111101n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit0001000000101001
32-bit00000000000000000001000000101001
64-bit0000000000000000000000000000000000000000000000000001000000101001
One's complement1110111111010110at 16 bits, every bit flipped
Bits reversed1001010000001000at 16 bits
Rotated left by 10010000001010010at 16 bits, wrapping
Shifted left by 110000001010010= 8,274, no wrap
Shifted right by 1100000010100= 2,068, discarding the low bit
These bits as a double2.04394958 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
4,137 to the power 217,114,769
4,137 to the power 370,803,799,353
4,137 to the power 4292,915,317,923,361
4,137 to the power 51,211,790,670,248,944,457
First ten multiples4,137, 8,274, 12,411, 16,548, 20,685, 24,822, 28,959, 33,096, 37,233, 41,370
Powers of twoBetween 2^12 (4,096) and 2^13 (8,192)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3Yes
Divisible by 4No, remainder 1
Divisible by 5No, remainder 2
Divisible by 6No, remainder 3
Divisible by 7Yes
Divisible by 8No, remainder 1
Divisible by 9No, remainder 6
Divisible by 10No, remainder 7
Divisible by 11No, remainder 1
Divisible by 12No, remainder 9
Divisible by 100No, remainder 37
Collatz (3n + 1) trajectory
Steps to reach 195the total stopping time
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps4,137 → 12,412 → 6,206 → 3,103 → 9,310 → 4,655 → 13,966 → 6,983 → 20,950 → 10,475 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage413,700%
4,137% as a decimal41.37
4,137% of 1004,137
4,137% of 1,00041,370
As a fraction of 1004,137/100
Read another way
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Derived from 4,137
Also reads as
4137 (year)
- Common year
- 365 days
- 42nd century
- Snake
4137 will be a common year of 365 days. It begins on a Tuesday and ends on a Tuesday. Easter Sunday falls on 21 April.
Structure of the year
Patterns forced by the calendar
Weekday counts52 of each, plus an extra Tuesday365 days is 52 weeks and 1 day, and the remainder starts on the weekday 1 January falls on
Sundays52
Mondays52
Tuesdays53one of the extras
Wednesdays52
Thursdays52
Fridays52
Saturdays52
Friday the 13th2 of them13 September, 13 December
ISO weeks52an ordinary 52-week year
Same calendar as4126the most recent year whose calendar is identical, so a printed one could be reused
Calendar repeats in4143, 4154, 41656 years later, then again after that; the gap is 6, 11 or 28 years, broken by centuries that skip a leap year
Months of 4137
January31 days, starts Tuesday
February28 days, starts Friday
August31 days, starts Thursday
September30 days, starts Sunday
October31 days, starts Tuesday
November30 days, starts Friday
December31 days, starts Sunday
Time references
These values depend on today’s date and change daily.
Unix timestamp at the start68,383,958,400
Unix timestamp at the end68,415,494,399
Years from now2,111 years from now
Days from today770,770 days to 1 January
The number 4137
As a number4,137
In wordsfour thousand, one hundred and thirty-seven
Roman numeralsNot defined above 3,999
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Also reads as
#441133 (colour)
- #441133
- Magenta
- Dark
- Nearest: Black
#441133 is a magenta with RGB values 68, 17, 51 and HSL 320°, 60%, 17%. It is a dark colour, so white text on it reaches 15.3:1 contrast (AAA for normal text). The nearest named colour is Black.
Colour values
#441133#441133
HEX#441133
HEX (short)#413
RGBrgb(68, 17, 51)
RGB (0–1)0.2667, 0.0667, 0.2
RGB percentages26.7%, 6.7%, 20%
HSLhsl(320, 60%, 16.7%)
HSV / HSBhsv(320, 75%, 26.7%)
CMYK0%, 75%, 25%, 73.3%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer4,460,851
CSS custom property--colour: #441133;
Brightness & contrast
Relative luminance0.01869WCAG 2.x, 0 is black and 1 is white
Perceived brightness43 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 15.29:1
Contrast with white15.29:1WCAG normal text: AAA
Contrast with black1.37:1WCAG normal text: Fail
Greyscale equivalent#1E1E1E
Inverted#BBEECC
Colour vision & accessibility
Distinguishable without hueYesnever rely on hue alone to carry meaning
Contrast with white, large text15.29:1WCAG large text: AAA
Contrast with black, large text1.37:1WCAG large text: Fail
Named colours
Hue familymagenta
CSS keyword usableNo exact keyword
Colour harmonies
Complementary#114422
Analogous#3B1144, #44111A
Triadic#334411, #113344
Split complementary#194411, #11443C
Tetradic#443B11, #114422, #111944
Tints, shades & saturation
Channel breakdown
R68
G17
B51
Red68 (26.7%)
Green17 (6.7%)
Blue51 (20%)
Hue320°
Saturation (HSL)60%
Lightness16.67%
Dominant channelRed
Hex per channelR 44 · G 11 · B 33
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Harmonies
Similar named colours
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