Recognised as Number

33,728

Positive
Even
Composite
5 digits

33,728 is an even 5-digit integer and a composite number. It has 28 divisors and a digital root of 5.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value33,728

Digit count5

Digit sum23

Digit product1,008

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

Digital root5repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^6 × 17 × 31

Distinct prime factors32, 17, 31

Number of divisors28

Sum of divisors σ(n)73,152

Aliquot sum39,424sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)15,360integers below n that share no factor with it

Carmichael function λ(n)240the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 15,360

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 8, 16, 17, 31, 32, 34, 62, 64, 68, 124, 136, 248, 272, 496, 527, 544, 992, 1,054, 1,088, 1,984, 2,108, 4,216, 8,432, 16,864, 33,72828 in total

Arithmetic

Previous number33,727

Next number33,729

Double67,456

Half16,864

Square1,137,577,984

Cube38,368,230,244,352

Square root183.651844532≈irrational, shown to 9 decimal places

Cube root32.309496963≈

Negation-33,728

Reciprocal0.000029649≈

Representations

Decimal33,728

Binary100000111100000016 bits

Octal101700

Hexadecimal83C0

Base 36Q0W

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

In wordsthirty-three thousand, seven hundred and twenty-eight

Ordinalthirty-three thousand, seven hundred and twenty-eighth

Scientific notation3.3728 × 10^4

Engineering notation33.728 × 10^3

In other bases

Ternary1201021012base 3; the most digit-efficient integer base after e: 10 digits

Quinary2034403base 5; one hand: 7 digits

Septenary200222base 7: 6 digits

Nonary51235base 9; each digit is two ternary digits: 5 digits

Duodecimal17628base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal4468base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:22:8base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT011T11TTdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000010011000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000001111000000

Bit length16 bitsto write the magnitude

Set bits5the population count, or Hamming weight

Zero bits11within that length

Bit parityodd5 set bits, so odd; not the same as the number itself being even

Highest set bitbit 15worth 32,768

Lowest set bitbit 66 trailing zeros

Power of twoNo

Bytes283 c0

Gray code1100001000100000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000001111000000

32-bit00000000000000001000001111000000

64-bit0000000000000000000000000000000000000000000000001000001111000000

One's complement0111110000111111at 16 bits, every bit flipped

Bits reversed0000001111000001at 16 bits

Rotated left by 10000011110000001at 16 bits, wrapping

Shifted left by 110000011110000000= 67,456, no wrap

Shifted right by 1100000111100000= 16,864, discarding the low bit

These bits as a double1.66638461 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,739+11

Previous prime33,721−7

Distance to nearest prime7

Nearest square below33,489

Nearest square above33,856

Powers & multiples

33,728 to the power 21,137,577,984

33,728 to the power 338,368,230,244,352

33,728 to the power 41,294,083,669,681,504,256

33,728 to the power 543,646,854,011,017,775,546,368

First ten multiples33,728, 67,456, 101,184, 134,912, 168,640, 202,368, 236,096, 269,824, 303,552, 337,280

Powers of twoBetween 2^15 (32,768) and 2^16 (65,536)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 2

Divisible by 4Yes

Divisible by 5No, remainder 3

Divisible by 6No, remainder 2

Divisible by 7No, remainder 2

Divisible by 8Yes

Divisible by 9No, remainder 5

Divisible by 10No, remainder 8

Divisible by 11No, remainder 2

Divisible by 12No, remainder 8

Divisible by 100No, remainder 28

Collatz (3n + 1) trajectory

Steps to reach 185the total stopping time

Highest value reached33,728

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

First steps33,728 → 16,864 → 8,432 → 4,216 → 2,108 → 1,054 → 527 → 1,582 → 791 → 2,374 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,372,800%

33,728% as a decimal337.28

33,728% of 10033,728

33,728% of 1,000337,280

As a fraction of 10033,728/100

Read another way

As seconds9 hours, 22 minutes and 8 seconds

As bytes32.938 KiB

As a 24-bit colour#0083C0

Keep nerding

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