Recognised as Number

33,884

Positive
Even
Composite
5 digits

33,884 is an even 5-digit integer and a composite number. It has 12 divisors and a digital root of 8.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value33,884

Digit count5

Digit sum26

Digit product2,304

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

Digital root8repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 43 × 197

Distinct prime factors32, 43, 197

Number of divisors12

Sum of divisors σ(n)60,984

Aliquot sum27,100sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)16,464integers below n that share no factor with it

Carmichael function λ(n)588the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 16,464

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 43, 86, 172, 197, 394, 788, 8,471, 16,942, 33,88412 in total

Arithmetic

Previous number33,883

Next number33,885

Double67,768

Half16,942

Square1,148,125,456

Cube38,903,082,951,104

Square root184.076071231≈irrational, shown to 9 decimal places

Cube root32.35923339≈

Negation-33,884

Reciprocal0.0000295125≈

Representations

Decimal33,884

Binary100001000101110016 bits

Octal102134

Hexadecimal845C

Base 36Q58

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

In wordsthirty-three thousand, eight hundred and eighty-four

Ordinalthirty-three thousand, eight hundred and eighty-fourth

Scientific notation3.3884 × 10^4

Engineering notation33.884 × 10^3

In other bases

Ternary1201110222base 3; the most digit-efficient integer base after e: 10 digits

Quinary2041014base 5; one hand: 7 digits

Septenary200534base 7: 6 digits

Nonary51428base 9; each digit is two ternary digits: 5 digits

Duodecimal17738base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal44e4base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:24:44base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT0111100Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000010110101100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000010001011100

Bit length16 bitsto write the magnitude

Set bits6the population count, or Hamming weight

Zero bits10within that length

Bit parityeven6 set bits, so even; not the same as the number itself being even

Highest set bitbit 15worth 32,768

Lowest set bitbit 22 trailing zeros

Power of twoNo

Bytes284 5c

Gray code1100011001110010n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000010001011100

32-bit00000000000000001000010001011100

64-bit0000000000000000000000000000000000000000000000001000010001011100

One's complement0111101110100011at 16 bits, every bit flipped

Bits reversed0011101000100001at 16 bits

Rotated left by 10000100010111001at 16 bits, wrapping

Shifted left by 110000100010111000= 67,768, no wrap

Shifted right by 1100001000101110= 16,942, discarding the low bit

These bits as a double1.67409203 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,889+5

Previous prime33,871−13

Distance to nearest prime5

Nearest square below33,856

Nearest square above34,225

Powers & multiples

33,884 to the power 21,148,125,456

33,884 to the power 338,903,082,951,104

33,884 to the power 41,318,192,062,715,207,936

33,884 to the power 544,665,619,853,042,105,703,424

First ten multiples33,884, 67,768, 101,652, 135,536, 169,420, 203,304, 237,188, 271,072, 304,956, 338,840

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 4

Divisible by 6No, remainder 2

Divisible by 7No, remainder 4

Divisible by 8No, remainder 4

Divisible by 9No, remainder 8

Divisible by 10No, remainder 4

Divisible by 11No, remainder 4

Divisible by 12No, remainder 8

Divisible by 100No, remainder 84

Collatz (3n + 1) trajectory

Steps to reach 159the total stopping time

Highest value reached57,1841× the starting value

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

First steps33,884 → 16,942 → 8,471 → 25,414 → 12,707 → 38,122 → 19,061 → 57,184 → 28,592 → 14,296 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,388,400%

33,884% as a decimal338.84

33,884% of 10033,884

33,884% of 1,000338,840

As a fraction of 10033,884/100

Read another way

As seconds9 hours, 24 minutes and 44 seconds

As bytes33.09 KiB

As a 24-bit colour#00845C

Keep nerding

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