Recognised as Number

27

Positive
Odd
Composite
Perfect cube
2 digits

27 is an odd 2-digit integer and a composite number. It has 4 divisors and a digital root of 9.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value27

Digit count2

Digit sum9

Digit product14

Multiplicative persistence2times the digit product can be taken before one digit is left

Digital root9repeated digit sum

PalindromicNoreads differently backwards

Perfect cubeYes, 3³

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation3^3

Distinct prime factors13

Number of divisors4

Sum of divisors σ(n)40

Aliquot sum13sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)18integers below n that share no factor with it

Carmichael function λ(n)18the smallest exponent with aˣ ≡ 1 for every unit coprime to n

Möbius function μ(n)0zero, because a prime divides n twice

SquarefreeNohas a repeated prime factor

All divisors1, 3, 9, 274 in total

Arithmetic

Previous number26

Next number28

Double54

Half13.5

Square729

Cube19,683

Square root5.196152423≈irrational, shown to 9 decimal places

Cube root3

Negation-27

Reciprocal0.037037037≈

27 factorial10,888,869,450,418,352,160,768,000,000

Representations

Decimal27

Binary110115 bits

Octal33

Hexadecimal1B

Base 36R

Roman numeralXXVII

In wordstwenty-seven

Ordinaltwenty-seventh

Scientific notation2.7 × 10^1

Engineering notation27

In other bases

Ternary1000base 3; the most digit-efficient integer base after e: 4 digits

Quinary102base 5; one hand: 3 digits

Septenary36base 7: 2 digits

Nonary30base 9; each digit is two ternary digits: 2 digits

Duodecimal23base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits

Vigesimal17base 20; hands and feet, and the Mayan and Yoruba systems: 2 digits

Sexagesimal27base 60; Babylonian, and still how an hour and a circle are divided: 1 digit

Balanced ternary1000digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary1101111base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00011011

Bit length5 bitsto write the magnitude

Set bits4the population count, or Hamming weight

Zero bits1within that length

Bit parityeven4 set bits, so even; not the same as the number itself being odd

Highest set bitbit 4worth 16

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes11b

Gray code10110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

8-bit00011011

16-bit0000000000011011

32-bit00000000000000000000000000011011

64-bit0000000000000000000000000000000000000000000000000000000000011011

One's complement11100100at 8 bits, every bit flipped

Bits reversed11011000at 8 bits

Rotated left by 100110110at 8 bits, wrapping

Shifted left by 1110110= 54, no wrap

Shifted right by 11101= 13, discarding the low bit

These bits as a double1.33397724 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime29+2

Previous prime23−4

Distance to nearest prime2

Nearest square below25

Nearest square above36

Powers & multiples

27 to the power 2729

27 to the power 319,683

27 to the power 4531,441

27 to the power 514,348,907

First ten multiples27, 54, 81, 108, 135, 162, 189, 216, 243, 270

Powers of twoBetween 2^4 (16) and 2^5 (32)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 3

Divisible by 5No, remainder 2

Divisible by 6No, remainder 3

Divisible by 7No, remainder 6

Divisible by 8No, remainder 3

Divisible by 9Yes

Divisible by 10No, remainder 7

Divisible by 11No, remainder 5

Divisible by 12No, remainder 3

Divisible by 100No, remainder 27

Collatz (3n + 1) trajectory

Steps to reach 1111the total stopping time

Highest value reached9,232341× the starting value

Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven

First steps27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,700%

27% as a decimal0.27

27% of 10027

27% of 1,000270

As a fraction of 10027/100

Read another way

As seconds27 seconds

As bytes27 B

As a 24-bit colour#00001B

Keep nerding

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