Recognised as Number

73,437

Positive
Odd
Composite
5 digits

73,437 is an odd 5-digit integer and a composite number. It has 16 divisors and a digital root of 6.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value73,437

Digit count5

Digit sum24

Digit product1,764

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

Digital root6repeated digit sum

PalindromicYesreads the same backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation3 × 7 × 13 × 269

Distinct prime factors43, 7, 13, 269

Number of divisors16

Sum of divisors σ(n)120,960

Aliquot sum47,523sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)38,592integers below n that share no factor with it

Carmichael function λ(n)804the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 38,592

Möbius function μ(n)+14 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 3, 7, 13, 21, 39, 91, 269, 273, 807, 1,883, 3,497, 5,649, 10,491, 24,479, 73,43716 in total

Arithmetic

Previous number73,436

Next number73,438

Double146,874

Half36,718.5

Square5,392,992,969

Cube396,045,224,664,453

Square root270.992619826≈irrational, shown to 9 decimal places

Cube root41.87662205≈

Negation-73,437

Reciprocal0.0000136171≈

Representations

Decimal73,437

Binary1000111101101110117 bits

Octal217335

Hexadecimal11EDD

Base 361KNX

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

In wordsseventy-three thousand, four hundred and thirty-seven

Ordinalseventy-three thousand, four hundred and thirty-seventh

Scientific notation7.3437 × 10^4

Engineering notation73.437 × 10^3

In other bases

Ternary10201201220base 3; the most digit-efficient integer base after e: 11 digits

Quinary4322222base 5; one hand: 7 digits

Septenary424050base 7: 6 digits

Nonary121656base 9; each digit is two ternary digits: 6 digits

Duodecimal365b9base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal93bhbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal20:23:57base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary11T1TT1T0T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary10110001100101101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000000010001111011011101

Bit length17 bitsto write the magnitude

Set bits11the population count, or Hamming weight

Zero bits6within that length

Bit parityodd11 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 16worth 65,536

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes301 1e dd

Gray code11001000110110011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000000010001111011011101

64-bit0000000000000000000000000000000000000000000000010001111011011101

One's complement11111111111111101110000100100010at 32 bits, every bit flipped

Bits reversed10111011011110001000000000000000at 32 bits

Rotated left by 100000000000000100011110110111010at 32 bits, wrapping

Shifted left by 1100011110110111010= 146,874, no wrap

Shifted right by 11000111101101110= 36,718, discarding the low bit

These bits as a double3.62826988 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime73,453+16

Previous prime73,433−4

Distance to nearest prime4

Nearest square below72,900

Nearest square above73,441

Powers & multiples

73,437 to the power 25,392,992,969

73,437 to the power 3396,045,224,664,453

73,437 to the power 429,084,373,163,683,434,961

73,437 to the power 52,135,869,112,021,420,413,230,957

First ten multiples73,437, 146,874, 220,311, 293,748, 367,185, 440,622, 514,059, 587,496, 660,933, 734,370

Powers of twoBetween 2^16 (65,536) and 2^17 (131,072)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 1

Divisible by 5No, remainder 2

Divisible by 6No, remainder 3

Divisible by 7Yes

Divisible by 8No, remainder 5

Divisible by 9No, remainder 6

Divisible by 10No, remainder 7

Divisible by 11No, remainder 1

Divisible by 12No, remainder 9

Divisible by 100No, remainder 37

Collatz (3n + 1) trajectory

Steps to reach 163the total stopping time

Highest value reached220,3123× the starting value

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

First steps73,437 → 220,312 → 110,156 → 55,078 → 27,539 → 82,618 → 41,309 → 123,928 → 61,964 → 30,982 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage7,343,700%

73,437% as a decimal734.37

73,437% of 10073,437

73,437% of 1,000734,370

As a fraction of 10073,437/100

Read another way

As seconds20 hours, 23 minutes and 57 seconds

As bytes71.716 KiB

As a 24-bit colour#011EDD

Keep nerding

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