Recognised as Number

27,140

Positive
Even
Composite
5 digits

27,140 is an even 5-digit integer and a composite number. It has 24 divisors and a digital root of 5.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value27,140

Digit count5

Digit sum14

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times the digit product can be taken before one digit is left

Digital root5repeated digit sum

PalindromicNoreads differently backwards

Happy numberYessquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 5 × 23 × 59

Distinct prime factors42, 5, 23, 59

Number of divisors24

Sum of divisors σ(n)60,480

Aliquot sum33,340sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)10,208integers below n that share no factor with it

Carmichael function λ(n)1,276the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 10,208

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 5, 10, 20, 23, 46, 59, 92, 115, 118, 230, 236, 295, 460, 590, 1,180, 1,357, 2,714, 5,428, 6,785, 13,570, 27,14024 in total

Arithmetic

Previous number27,139

Next number27,141

Double54,280

Half13,570

Square736,579,600

Cube19,990,770,344,000

Square root164.742222882≈irrational, shown to 9 decimal places

Cube root30.051762489≈

Negation-27,140

Reciprocal0.000036846≈

Representations

Decimal27,140

Binary11010100000010015 bits

Octal65004

Hexadecimal6A04

Base 36KXW

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

In wordstwenty-seven thousand, one hundred and forty

Ordinaltwenty-seven thousand, one hundred and fortieth

Scientific notation2.714 × 10^4

Engineering notation27.14 × 10^3

In other bases

Ternary1101020012base 3; the most digit-efficient integer base after e: 10 digits

Quinary1332030base 5; one hand: 7 digits

Septenary142061base 7: 6 digits

Nonary41205base 9; each digit is two ternary digits: 5 digits

Duodecimal13858base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal37h0base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal7:32:20base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary11011T01TTdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11011111000000100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0110101000000100

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 22 trailing zeros

Power of twoNo

Bytes26a 04

Gray code101111100000110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0110101000000100

32-bit00000000000000000110101000000100

64-bit0000000000000000000000000000000000000000000000000110101000000100

One's complement1001010111111011at 16 bits, every bit flipped

Bits reversed0010000001010110at 16 bits

Rotated left by 11101010000001000at 16 bits, wrapping

Shifted left by 11101010000001000= 54,280, no wrap

Shifted right by 111010100000010= 13,570, discarding the low bit

These bits as a double1.34089416 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime27,143+3

Previous prime27,127−13

Distance to nearest prime3

Nearest square below26,896

Nearest square above27,225

Powers & multiples

27,140 to the power 2736,579,600

27,140 to the power 319,990,770,344,000

27,140 to the power 4542,549,507,136,160,000

27,140 to the power 514,724,793,623,675,382,400,000

First ten multiples27,140, 54,280, 81,420, 108,560, 135,700, 162,840, 189,980, 217,120, 244,260, 271,400

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

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 2

Divisible by 4Yes

Divisible by 5Yes

Divisible by 6No, remainder 2

Divisible by 7No, remainder 1

Divisible by 8No, remainder 4

Divisible by 9No, remainder 5

Divisible by 10Yes

Divisible by 11No, remainder 3

Divisible by 12No, remainder 8

Divisible by 100No, remainder 40

Collatz (3n + 1) trajectory

Steps to reach 190the total stopping time

Highest value reached28,9961× the starting value

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

First steps27,140 → 13,570 → 6,785 → 20,356 → 10,178 → 5,089 → 15,268 → 7,634 → 3,817 → 11,452 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,714,000%

27,140% as a decimal271.4

27,140% of 10027,140

27,140% of 1,000271,400

As a fraction of 10027,140/100

Read another way

As seconds7 hours, 32 minutes and 20 seconds

As bytes26.504 KiB

As a 24-bit colour#006A04

Keep nerding

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