Recognised as Number

27,138

Positive
Even
Composite
5 digits

27,138 is an even 5-digit integer and a composite number. It has 8 divisors and a digital root of 3.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value27,138

Digit count5

Digit sum21

Digit product336

Multiplicative persistence4times the digit product can be taken before one digit is left

Digital root3repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2 × 3 × 4,523

Distinct prime factors32, 3, 4,523

Number of divisors8

Sum of divisors σ(n)54,288

Aliquot sum27,150sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)9,044integers below n that share no factor with it

Carmichael function λ(n)4,522the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 9,044

Möbius function μ(n)−13 distinct prime factors, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 2, 3, 6, 4,523, 9,046, 13,569, 27,1388 in total

Arithmetic

Previous number27,137

Next number27,139

Double54,276

Half13,569

Square736,471,044

Cube19,986,351,192,072

Square root164.736152681≈irrational, shown to 9 decimal places

Cube root30.051024279≈

Negation-27,138

Reciprocal0.0000368487≈

Representations

Decimal27,138

Binary11010100000001015 bits

Octal65002

Hexadecimal6A02

Base 36KXU

Roman numeralNot defined above 3,999there is no agreed standard notation

In wordstwenty-seven thousand, one hundred and thirty-eight

Ordinaltwenty-seven thousand, one hundred and thirty-eighth

Scientific notation2.7138 × 10^4

Engineering notation27.138 × 10^3

In other bases

Ternary1101020010base 3; the most digit-efficient integer base after e: 10 digits

Quinary1332023base 5; one hand: 7 digits

Septenary142056base 7: 6 digits

Nonary41203base 9; each digit is two ternary digits: 5 digits

Duodecimal13856base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal37gibase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal7:32:18base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary11011T0010digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11011111000000110base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0110101000000010

Bit length15 bitsto write the magnitude

Set bits5the population count, or Hamming weight

Zero bits10within that length

Bit parityodd5 set bits, so odd; not the same as the number itself being even

Highest set bitbit 14worth 16,384

Lowest set bitbit 11 trailing zero

Power of twoNo

Bytes26a 02

Gray code101111100000011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0110101000000010

32-bit00000000000000000110101000000010

64-bit0000000000000000000000000000000000000000000000000110101000000010

One's complement1001010111111101at 16 bits, every bit flipped

Bits reversed0100000001010110at 16 bits

Rotated left by 11101010000000100at 16 bits, wrapping

Shifted left by 11101010000000100= 54,276, no wrap

Shifted right by 111010100000001= 13,569, discarding the low bit

These bits as a double1.34079535 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime27,143+5

Previous prime27,127−11

Distance to nearest prime5

Nearest square below26,896

Nearest square above27,225

Powers & multiples

27,138 to the power 2736,471,044

27,138 to the power 319,986,351,192,072

27,138 to the power 4542,389,598,650,449,936

27,138 to the power 514,719,368,928,175,910,363,168

First ten multiples27,138, 54,276, 81,414, 108,552, 135,690, 162,828, 189,966, 217,104, 244,242, 271,380

Powers of twoBetween 2^14 (16,384) and 2^15 (32,768)

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4No, remainder 2

Divisible by 5No, remainder 3

Divisible by 6Yes

Divisible by 7No, remainder 6

Divisible by 8No, remainder 2

Divisible by 9No, remainder 3

Divisible by 10No, remainder 8

Divisible by 11No, remainder 1

Divisible by 12No, remainder 6

Divisible by 100No, remainder 38

Collatz (3n + 1) trajectory

Steps to reach 138the total stopping time

Highest value reached40,7081× the starting value

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

First steps27,138 → 13,569 → 40,708 → 20,354 → 10,177 → 30,532 → 15,266 → 7,633 → 22,900 → 11,450 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,713,800%

27,138% as a decimal271.38

27,138% of 10027,138

27,138% of 1,000271,380

As a fraction of 10027,138/100

Read another way

As seconds7 hours, 32 minutes and 18 seconds

As bytes26.502 KiB

As a 24-bit colour#006A02

Keep nerding

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