Recognised as Number

29,729

Positive
Odd
Composite
5 digits

29,729 is an odd 5-digit integer and a composite number. It has 8 divisors and a digital root of 2.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value29,729

Digit count5

Digit sum29

Digit product2,268

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

Digital root2repeated digit sum

PalindromicNoreads differently backwards

Happy numberYessquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation7 × 31 × 137

Distinct prime factors37, 31, 137

Number of divisors8

Sum of divisors σ(n)35,328

Aliquot sum5,599sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)24,480integers below n that share no factor with it

Carmichael function λ(n)2,040the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 24,480

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

SquarefreeYesno repeated prime factor

All divisors1, 7, 31, 137, 217, 959, 4,247, 29,7298 in total

Arithmetic

Previous number29,728

Next number29,730

Double59,458

Half14,864.5

Square883,813,441

Cube26,274,889,787,489

Square root172.420996401≈irrational, shown to 9 decimal places

Cube root30.978479688≈

Negation-29,729

Reciprocal0.0000336372≈

Representations

Decimal29,729

Binary11101000010000115 bits

Octal72041

Hexadecimal7421

Base 36MXT

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

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

Ordinaltwenty-nine thousand, seven hundred and twenty-ninth

Scientific notation2.9729 × 10^4

Engineering notation29.729 × 10^3

In other bases

Ternary1111210002base 3; the most digit-efficient integer base after e: 10 digits

Quinary1422404base 5; one hand: 7 digits

Septenary152450base 7: 6 digits

Nonary44702base 9; each digit is two ternary digits: 5 digits

Duodecimal15255base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal3e69base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal8:15:29base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TTTTT1001Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11011010001100001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0111010000100001

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 odd

Highest set bitbit 14worth 16,384

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes274 21

Gray code100111000110001n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0111010000100001

32-bit00000000000000000111010000100001

64-bit0000000000000000000000000000000000000000000000000111010000100001

One's complement1000101111011110at 16 bits, every bit flipped

Bits reversed1000010000101110at 16 bits

Rotated left by 11110100001000010at 16 bits, wrapping

Shifted left by 11110100001000010= 59,458, no wrap

Shifted right by 111101000010000= 14,864, discarding the low bit

These bits as a double1.46880776 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime29,741+12

Previous prime29,723−6

Distance to nearest prime6

Nearest square below29,584

Nearest square above29,929

Powers & multiples

29,729 to the power 2883,813,441

29,729 to the power 326,274,889,787,489

29,729 to the power 4781,126,198,492,260,481

29,729 to the power 523,222,100,754,976,411,839,649

First ten multiples29,729, 59,458, 89,187, 118,916, 148,645, 178,374, 208,103, 237,832, 267,561, 297,290

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 4

Divisible by 6No, remainder 5

Divisible by 7Yes

Divisible by 8No, remainder 1

Divisible by 9No, remainder 2

Divisible by 10No, remainder 9

Divisible by 11No, remainder 7

Divisible by 12No, remainder 5

Divisible by 100No, remainder 29

Collatz (3n + 1) trajectory

Steps to reach 1121the total stopping time

Highest value reached214,3247× the starting value

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

First steps29,729 → 89,188 → 44,594 → 22,297 → 66,892 → 33,446 → 16,723 → 50,170 → 25,085 → 75,256 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,972,900%

29,729% as a decimal297.29

29,729% of 10029,729

29,729% of 1,000297,290

As a fraction of 10029,729/100

Read another way

As seconds8 hours, 15 minutes and 29 seconds

As bytes29.032 KiB

As a 24-bit colour#007421

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