Recognised as Number

33,888

Positive
Even
Composite
5 digits

33,888 is an even 5-digit integer and a composite number. It has 24 divisors and a digital root of 3.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value33,888

Digit count5

Digit sum30

Digit product4,608

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

Digital root3repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^5 × 3 × 353

Distinct prime factors32, 3, 353

Number of divisors24

Sum of divisors σ(n)89,208

Aliquot sum55,320sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)11,264integers below n that share no factor with it

Carmichael function λ(n)352the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 11,264

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 353, 706, 1,059, 1,412, 2,118, 2,824, 4,236, 5,648, 8,472, 11,296, 16,944, 33,88824 in total

Arithmetic

Previous number33,887

Next number33,889

Double67,776

Half16,944

Square1,148,396,544

Cube38,916,862,083,072

Square root184.086935984≈irrational, shown to 9 decimal places

Cube root32.360506673≈

Negation-33,888

Reciprocal0.000029509≈

Representations

Decimal33,888

Binary100001000110000016 bits

Octal102140

Hexadecimal8460

Base 36Q5C

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

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

Ordinalthirty-three thousand, eight hundred and eighty-eighth

Scientific notation3.3888 × 10^4

Engineering notation33.888 × 10^3

In other bases

Ternary1201111010base 3; the most digit-efficient integer base after e: 10 digits

Quinary2041023base 5; one hand: 7 digits

Septenary200541base 7: 6 digits

Nonary51433base 9; each digit is two ternary digits: 5 digits

Duodecimal17740base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal44e8base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:24:48base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT01111010digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000010110100000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000010001100000

Bit length16 bitsto write the magnitude

Set bits4the population count, or Hamming weight

Zero bits12within that length

Bit parityeven4 set bits, so even; not the same as the number itself being even

Highest set bitbit 15worth 32,768

Lowest set bitbit 55 trailing zeros

Power of twoNo

Bytes284 60

Gray code1100011001010000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000010001100000

32-bit00000000000000001000010001100000

64-bit0000000000000000000000000000000000000000000000001000010001100000

One's complement0111101110011111at 16 bits, every bit flipped

Bits reversed0000011000100001at 16 bits

Rotated left by 10000100011000001at 16 bits, wrapping

Shifted left by 110000100011000000= 67,776, no wrap

Shifted right by 1100001000110000= 16,944, discarding the low bit

These bits as a double1.67428966 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,889+1

Previous prime33,871−17

Distance to nearest prime1

Nearest square below33,856

Nearest square above34,225

Powers & multiples

33,888 to the power 21,148,396,544

33,888 to the power 338,916,862,083,072

33,888 to the power 41,318,814,622,271,143,936

33,888 to the power 544,691,989,919,524,525,703,168

First ten multiples33,888, 67,776, 101,664, 135,552, 169,440, 203,328, 237,216, 271,104, 304,992, 338,880

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

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5No, remainder 3

Divisible by 6Yes

Divisible by 7No, remainder 1

Divisible by 8Yes

Divisible by 9No, remainder 3

Divisible by 10No, remainder 8

Divisible by 11No, remainder 8

Divisible by 12Yes

Divisible by 100No, remainder 88

Collatz (3n + 1) trajectory

Steps to reach 136the total stopping time

Highest value reached33,888

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

First steps33,888 → 16,944 → 8,472 → 4,236 → 2,118 → 1,059 → 3,178 → 1,589 → 4,768 → 2,384 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,388,800%

33,888% as a decimal338.88

33,888% of 10033,888

33,888% of 1,000338,880

As a fraction of 10033,888/100

Read another way

As seconds9 hours, 24 minutes and 48 seconds

As bytes33.094 KiB

As a 24-bit colour#008460

Keep nerding

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