Recognised as Number

29,727

Positive
Odd
Composite
5 digits

29,727 is an odd 5-digit integer and a composite number. It has 10 divisors and a digital root of 9.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value29,727

Digit count5

Digit sum27

Digit product1,764

Multiplicative persistence5times the digit product can be taken before one digit is left

Digital root9repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation3^4 × 367

Distinct prime factors23, 367

Number of divisors10

Sum of divisors σ(n)44,528

Aliquot sum14,801sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)19,764integers below n that share no factor with it

Carmichael function λ(n)3,294the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 19,764

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

SquarefreeNohas a repeated prime factor

All divisors1, 3, 9, 27, 81, 367, 1,101, 3,303, 9,909, 29,72710 in total

Arithmetic

Previous number29,726

Next number29,728

Double59,454

Half14,863.5

Square883,694,529

Cube26,269,587,263,583

Square root172.415196546≈irrational, shown to 9 decimal places

Cube root30.977784986≈

Negation-29,727

Reciprocal0.0000336395≈

Representations

Decimal29,727

Binary11101000001111115 bits

Octal72037

Hexadecimal741F

Base 36MXR

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

In wordstwenty-nine thousand, seven hundred and twenty-seven

Ordinaltwenty-nine thousand, seven hundred and twenty-seventh

Scientific notation2.9727 × 10^4

Engineering notation29.727 × 10^3

In other bases

Ternary1111210000base 3; the most digit-efficient integer base after e: 10 digits

Quinary1422402base 5; one hand: 7 digits

Septenary152445base 7: 6 digits

Nonary44700base 9; each digit is two ternary digits: 5 digits

Duodecimal15253base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal3e67base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal8:15:27base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TTTTT10000digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11011010001100011base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0111010000011111

Bit length15 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits6within that length

Bit parityodd9 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

Bytes274 1f

Gray code100111000010000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0111010000011111

32-bit00000000000000000111010000011111

64-bit0000000000000000000000000000000000000000000000000111010000011111

One's complement1000101111100000at 16 bits, every bit flipped

Bits reversed1111100000101110at 16 bits

Rotated left by 11110100000111110at 16 bits, wrapping

Shifted left by 11110100000111110= 59,454, no wrap

Shifted right by 111101000001111= 14,863, discarding the low bit

These bits as a double1.46870895 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime29,741+14

Previous prime29,723−4

Distance to nearest prime4

Nearest square below29,584

Nearest square above29,929

Powers & multiples

29,727 to the power 2883,694,529

29,727 to the power 326,269,587,263,583

29,727 to the power 4780,916,020,584,531,841

29,727 to the power 523,214,290,543,916,378,037,407

First ten multiples29,727, 59,454, 89,181, 118,908, 148,635, 178,362, 208,089, 237,816, 267,543, 297,270

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

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 5

Divisible by 8No, remainder 7

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 1147the total stopping time

Highest value reached857,14028× the starting value

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

First steps29,727 → 89,182 → 44,591 → 133,774 → 66,887 → 200,662 → 100,331 → 300,994 → 150,497 → 451,492 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,972,700%

29,727% as a decimal297.27

29,727% of 10029,727

29,727% of 1,000297,270

As a fraction of 10029,727/100

Read another way

As seconds8 hours, 15 minutes and 27 seconds

As bytes29.03 KiB

As a 24-bit colour#00741F

Keep nerding

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