Recognised as Number
420
- Positive
- Even
- Composite
- 3 digits
420 is an even 3-digit integer and a composite number. It has 24 divisors and a digital root of 6.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value420
Digit count3
Digit sum6
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times 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 numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^2 × 3 × 5 × 7
Distinct prime factors42, 3, 5, 7
Number of divisors24
Sum of divisors σ(n)1,344
Aliquot sum924sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)96integers below n that share no factor with it
Carmichael function λ(n)12the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 96
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 42024 in total
Arithmetic
Representations
Decimal420
Binary1101001009 bits
Octal644
Hexadecimal1A4
Base 36BO
Roman numeralCDXX
In wordsfour hundred and twenty
Ordinalfour hundred and twentieth
Scientific notation4.2 × 10^2
Engineering notation420
In other bases
Ternary120120base 3; the most digit-efficient integer base after e — 6 digits
Quinary3140base 5; one hand — 4 digits
Septenary1140base 7 — 4 digits
Nonary516base 9; each digit is two ternary digits — 3 digits
Duodecimal2b0base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves — 3 digits
Vigesimal110base 20; hands and feet, and the Mayan and Yoruba systems — 3 digits
Sexagesimal7:0base 60; Babylonian, and still how an hour and a circle are divided — 2 digits
Balanced ternary1TT1TT0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary11011100100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0000000110100100
Bit length9 bitsto write the magnitude
Set bits4the population count, or Hamming weight
Zero bits5within that length
Bit parityeven4 set bits, so even; not the same as the number itself being even
Highest set bitbit 8worth 256
Lowest set bitbit 22 trailing zeros
Power of twoNo
Bytes201 a4
Gray code101110110n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit0000000110100100
32-bit00000000000000000000000110100100
64-bit0000000000000000000000000000000000000000000000000000000110100100
One's complement1111111001011011at 16 bits, every bit flipped
Bits reversed0010010110000000at 16 bits
Rotated left by 10000001101001000at 16 bits, wrapping
Shifted left by 11101001000= 840, no wrap
Shifted right by 111010010= 210, discarding the low bit
These bits as a double2.07507571 × 10^-321≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
420 to the power 2176,400
420 to the power 374,088,000
420 to the power 431,116,960,000
420 to the power 513,069,123,200,000
First ten multiples420, 840, 1,260, 1,680, 2,100, 2,520, 2,940, 3,360, 3,780, 4,200
Powers of twoBetween 2^8 (256) and 2^9 (512)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6Yes
Divisible by 7Yes
Divisible by 8No, remainder 4
Divisible by 9No, remainder 6
Divisible by 10Yes
Divisible by 11No, remainder 2
Divisible by 12Yes
Divisible by 100No, remainder 20
Collatz (3n + 1) trajectory
Steps to reach 140the total stopping time
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps420 → 210 → 105 → 316 → 158 → 79 → 238 → 119 → 358 → 179 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage42,000%
420% as a decimal4.2
420% of 100420
420% of 1,0004,200
As a fraction of 100420/100
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Derived from 420
Other readings
Also reads as
#442200 (colour)
- #442200
- Orange
- Dark
- Nearest: Saddle brown
#442200 is a orange with RGB values 68, 34, 0 and HSL 30°, 100%, 13%. It is a dark colour, so white text on it reaches 14.2:1 contrast (AAA for normal text). The nearest named colour is Saddle brown.
Colour values
#442200#442200
HEX#442200
HEX (short)#420
RGBrgb(68, 34, 0)
RGB (0–1)0.2667, 0.1333, 0
RGB percentages26.7%, 13.3%, 0%
HSLhsl(30, 100%, 13.3%)
HSV / HSBhsv(30, 100%, 26.7%)
CMYK0%, 50%, 100%, 73.3%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer4,465,152
CSS custom property--colour: #442200;
Brightness & contrast
Relative luminance0.02373WCAG 2.x, 0 is black and 1 is white
Perceived brightness45.4 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 14.24:1
Contrast with white14.24:1WCAG normal text: AAA
Contrast with black1.47:1WCAG normal text: Fail
Greyscale equivalent#272727
Inverted#BBDDFF
Colour vision & accessibility
Distinguishable without hueYesnever rely on hue alone to carry meaning
Contrast with white, large text14.24:1WCAG large text: AAA
Contrast with black, large text1.47:1WCAG large text: Fail
Named colours
Hue familyorange
CSS keyword usableNo exact keyword
Colour harmonies
Complementary#002244
Analogous#440000, #444400
Triadic#004422, #220044
Split complementary#004444, #000044
Tetradic#004400, #002244, #440044
Tints, shades & saturation
Channel breakdown
R68
G34
B0
Red68 (26.7%)
Green34 (13.3%)
Blue0 (0%)
Hue30°
Saturation (HSL)100%
Lightness13.33%
Dominant channelRed
Hex per channelR 44 · G 22 · B 00
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