Recognised as Number

27,142

Positive
Even
Composite
5 digits

27,142 is an even 5-digit integer and a composite number. It has 8 divisors and a digital root of 7.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value27,142

Digit count5

Digit sum16

Digit product112

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

Digital root7repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2 × 41 × 331

Distinct prime factors32, 41, 331

Number of divisors8

Sum of divisors σ(n)41,832

Aliquot sum14,690sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)13,200integers below n that share no factor with it

Carmichael function λ(n)1,320the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 13,200

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

SquarefreeYesno repeated prime factor

All divisors1, 2, 41, 82, 331, 662, 13,571, 27,1428 in total

Arithmetic

Previous number27,141

Next number27,143

Double54,284

Half13,571

Square736,688,164

Cube19,995,190,147,288

Square root164.748292859≈irrational, shown to 9 decimal places

Cube root30.052500662≈

Negation-27,142

Reciprocal0.0000368433≈

Representations

Decimal27,142

Binary11010100000011015 bits

Octal65006

Hexadecimal6A06

Base 36KXY

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

In wordstwenty-seven thousand, one hundred and forty-two

Ordinaltwenty-seven thousand, one hundred and forty-second

Scientific notation2.7142 × 10^4

Engineering notation27.142 × 10^3

In other bases

Ternary1101020021base 3; the most digit-efficient integer base after e: 10 digits

Quinary1332032base 5; one hand: 7 digits

Septenary142063base 7: 6 digits

Nonary41207base 9; each digit is two ternary digits: 5 digits

Duodecimal1385abase 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal37h2base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal7:32:22base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary11011T01T1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11011111000011010base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0110101000000110

Bit length15 bitsto write the magnitude

Set bits6the population count, or Hamming weight

Zero bits9within that length

Bit parityeven6 set bits, so even; 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 06

Gray code101111100000101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0110101000000110

32-bit00000000000000000110101000000110

64-bit0000000000000000000000000000000000000000000000000110101000000110

One's complement1001010111111001at 16 bits, every bit flipped

Bits reversed0110000001010110at 16 bits

Rotated left by 11101010000001100at 16 bits, wrapping

Shifted left by 11101010000001100= 54,284, no wrap

Shifted right by 111010100000011= 13,571, discarding the low bit

These bits as a double1.34099298 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime27,143+1

Previous prime27,127−15

Distance to nearest prime1

Nearest square below26,896

Nearest square above27,225

Powers & multiples

27,142 to the power 2736,688,164

27,142 to the power 319,995,190,147,288

27,142 to the power 4542,709,450,977,690,896

27,142 to the power 514,730,219,918,436,486,299,232

First ten multiples27,142, 54,284, 81,426, 108,568, 135,710, 162,852, 189,994, 217,136, 244,278, 271,420

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

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 1

Divisible by 4No, remainder 2

Divisible by 5No, remainder 2

Divisible by 6No, remainder 4

Divisible by 7No, remainder 3

Divisible by 8No, remainder 6

Divisible by 9No, remainder 7

Divisible by 10No, remainder 2

Divisible by 11No, remainder 5

Divisible by 12No, remainder 10

Divisible by 100No, remainder 42

Collatz (3n + 1) trajectory

Steps to reach 190the total stopping time

Highest value reached61,0722× the starting value

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

First steps27,142 → 13,571 → 40,714 → 20,357 → 61,072 → 30,536 → 15,268 → 7,634 → 3,817 → 11,452 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,714,200%

27,142% as a decimal271.42

27,142% of 10027,142

27,142% of 1,000271,420

As a fraction of 10027,142/100

Read another way

As seconds7 hours, 32 minutes and 22 seconds

As bytes26.506 KiB

As a 24-bit colour#006A06

Keep nerding

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