Recognised as Number

33,360

Positive
Even
Composite
5 digits

33,360 is an even 5-digit integer and a composite number. It has 40 divisors and a digital root of 6.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value33,360

Digit count5

Digit sum15

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times the digit product can be taken before one digit is left

Digital root6repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^4 × 3 × 5 × 139

Distinct prime factors42, 3, 5, 139

Number of divisors40

Sum of divisors σ(n)104,160

Aliquot sum70,800sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)8,832integers below n that share no factor with it

Carmichael function λ(n)276the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 8,832

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 139, 240, 278, 417, 556, 695, 834, 1,112, 1,390, 1,668, 2,085, 2,224, 2,780, 3,336, 4,170, 5,560, 6,672, 8,340, 11,120, 16,680, 33,36040 in total

Arithmetic

Previous number33,359

Next number33,361

Double66,720

Half16,680

Square1,112,889,600

Cube37,125,997,056,000

Square root182.647200909≈irrational, shown to 9 decimal places

Cube root32.191559327≈

Negation-33,360

Reciprocal0.000029976≈

Representations

Decimal33,360

Binary100000100101000016 bits

Octal101120

Hexadecimal8250

Base 36PQO

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

In wordsthirty-three thousand, three hundred and sixty

Ordinalthirty-three thousand, three hundred and sixtieth

Scientific notation3.336 × 10^4

Engineering notation33.36 × 10^3

In other bases

Ternary1200202120base 3; the most digit-efficient integer base after e: 10 digits

Quinary2031420base 5; one hand: 7 digits

Septenary166155base 7: 6 digits

Nonary50676base 9; each digit is two ternary digits: 5 digits

Duodecimal17380base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal4380base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:16:0base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT01T10TT0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000011001010000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000001001010000

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 44 trailing zeros

Power of twoNo

Bytes282 50

Gray code1100001101111000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000001001010000

32-bit00000000000000001000001001010000

64-bit0000000000000000000000000000000000000000000000001000001001010000

One's complement0111110110101111at 16 bits, every bit flipped

Bits reversed0000101001000001at 16 bits

Rotated left by 10000010010100001at 16 bits, wrapping

Shifted left by 110000010010100000= 66,720, no wrap

Shifted right by 1100000100101000= 16,680, discarding the low bit

These bits as a double1.64820299 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,377+17

Previous prime33,359−1

Distance to nearest prime1

Nearest square below33,124

Nearest square above33,489

Powers & multiples

33,360 to the power 21,112,889,600

33,360 to the power 337,125,997,056,000

33,360 to the power 41,238,523,261,788,160,000

33,360 to the power 541,317,136,013,253,017,600,000

First ten multiples33,360, 66,720, 100,080, 133,440, 166,800, 200,160, 233,520, 266,880, 300,240, 333,600

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 5Yes

Divisible by 6Yes

Divisible by 7No, remainder 5

Divisible by 8Yes

Divisible by 9No, remainder 6

Divisible by 10Yes

Divisible by 11No, remainder 8

Divisible by 12Yes

Divisible by 100No, remainder 60

Collatz (3n + 1) trajectory

Steps to reach 1129the total stopping time

Highest value reached33,360

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

First steps33,360 → 16,680 → 8,340 → 4,170 → 2,085 → 6,256 → 3,128 → 1,564 → 782 → 391 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,336,000%

33,360% as a decimal333.6

33,360% of 10033,360

33,360% of 1,000333,600

As a fraction of 10033,360/100

Read another way

As seconds9 hours and 16 minutes

As bytes32.578 KiB

As a 24-bit colour#008250

Keep nerding

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