Recognised as Number

27,137

Positive
Odd
Composite
5 digits

27,137 is an odd 5-digit integer and a composite number. It has 4 divisors and a digital root of 2.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value27,137

Digit count5

Digit sum20

Digit product294

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

Digital root2repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation11 × 2,467

Distinct prime factors211, 2,467

Number of divisors4

Sum of divisors σ(n)29,616

Aliquot sum2,479sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)24,660integers below n that share no factor with it

Carmichael function λ(n)12,330the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 24,660

Möbius function μ(n)+12 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 11, 2,467, 27,1374 in total

Arithmetic

Previous number27,136

Next number27,138

Double54,274

Half13,568.5

Square736,416,769

Cube19,984,141,860,353

Square root164.733117496≈irrational, shown to 9 decimal places

Cube root30.050655161≈

Negation-27,137

Reciprocal0.0000368501≈

Representations

Decimal27,137

Binary11010100000000115 bits

Octal65001

Hexadecimal6A01

Base 36KXT

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

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

Ordinaltwenty-seven thousand, one hundred and thirty-seventh

Scientific notation2.7137 × 10^4

Engineering notation27.137 × 10^3

In other bases

Ternary1101020002base 3; the most digit-efficient integer base after e: 10 digits

Quinary1332022base 5; one hand: 7 digits

Septenary142055base 7: 6 digits

Nonary41202base 9; each digit is two ternary digits: 5 digits

Duodecimal13855base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal37ghbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal7:32:17base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary11011T001Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11011111000000001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0110101000000001

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 odd

Highest set bitbit 14worth 16,384

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes26a 01

Gray code101111100000001n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0110101000000001

32-bit00000000000000000110101000000001

64-bit0000000000000000000000000000000000000000000000000110101000000001

One's complement1001010111111110at 16 bits, every bit flipped

Bits reversed1000000001010110at 16 bits

Rotated left by 11101010000000010at 16 bits, wrapping

Shifted left by 11101010000000010= 54,274, no wrap

Shifted right by 111010100000000= 13,568, discarding the low bit

These bits as a double1.34074594 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime27,143+6

Previous prime27,127−10

Distance to nearest prime6

Nearest square below26,896

Nearest square above27,225

Powers & multiples

27,137 to the power 2736,416,769

27,137 to the power 319,984,141,860,353

27,137 to the power 4542,309,657,664,399,361

27,137 to the power 514,716,657,180,038,805,459,457

First ten multiples27,137, 54,274, 81,411, 108,548, 135,685, 162,822, 189,959, 217,096, 244,233, 271,370

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 2

Divisible by 6No, remainder 5

Divisible by 7No, remainder 5

Divisible by 8No, remainder 1

Divisible by 9No, remainder 2

Divisible by 10No, remainder 7

Divisible by 11Yes

Divisible by 12No, remainder 5

Divisible by 100No, remainder 37

Collatz (3n + 1) trajectory

Steps to reach 1139the total stopping time

Highest value reached81,4123× the starting value

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

First steps27,137 → 81,412 → 40,706 → 20,353 → 61,060 → 30,530 → 15,265 → 45,796 → 22,898 → 11,449 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,713,700%

27,137% as a decimal271.37

27,137% of 10027,137

27,137% of 1,000271,370

As a fraction of 10027,137/100

Read another way

As seconds7 hours, 32 minutes and 17 seconds

As bytes26.501 KiB

As a 24-bit colour#006A01

Keep nerding

Every link below is a page Nerdulator can generate from what it already knows about this value.