Recognised as Number

33,327

Positive
Odd
Composite
5 digits

33,327 is an odd 5-digit integer and a composite number. It has 18 divisors and a digital root of 9.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value33,327

Digit count5

Digit sum18

Digit product378

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

Digital root9repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation3^2 × 7 × 23^2

Distinct prime factors33, 7, 23

Number of divisors18

Sum of divisors σ(n)57,512

Aliquot sum24,185sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)18,216integers below n that share no factor with it

Carmichael function λ(n)1,518the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 18,216

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

SquarefreeNohas a repeated prime factor

All divisors1, 3, 7, 9, 21, 23, 63, 69, 161, 207, 483, 529, 1,449, 1,587, 3,703, 4,761, 11,109, 33,32718 in total

Arithmetic

Previous number33,326

Next number33,328

Double66,654

Half16,663.5

Square1,110,688,929

Cube37,015,929,936,783

Square root182.556840463≈irrational, shown to 9 decimal places

Cube root32.180941102≈

Negation-33,327

Reciprocal0.0000300057≈

Representations

Decimal33,327

Binary100000100010111116 bits

Octal101057

Hexadecimal822F

Base 36PPR

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

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

Ordinalthirty-three thousand, three hundred and twenty-seventh

Scientific notation3.3327 × 10^4

Engineering notation33.327 × 10^3

In other bases

Ternary1200201100base 3; the most digit-efficient integer base after e: 10 digits

Quinary2031302base 5; one hand: 7 digits

Septenary166110base 7: 6 digits

Nonary50640base 9; each digit is two ternary digits: 5 digits

Duodecimal17353base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal4367base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:15:27base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT01T01100digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000011001110011base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000001000101111

Bit length16 bitsto write the magnitude

Set bits7the population count, or Hamming weight

Zero bits9within that length

Bit parityodd7 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 15worth 32,768

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes282 2f

Gray code1100001100111000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000001000101111

32-bit00000000000000001000001000101111

64-bit0000000000000000000000000000000000000000000000001000001000101111

One's complement0111110111010000at 16 bits, every bit flipped

Bits reversed1111010001000001at 16 bits

Rotated left by 10000010001011111at 16 bits, wrapping

Shifted left by 110000010001011110= 66,654, no wrap

Shifted right by 1100000100010111= 16,663, discarding the low bit

These bits as a double1.64657258 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,329+2

Previous prime33,317−10

Distance to nearest prime2

Nearest square below33,124

Nearest square above33,489

Powers & multiples

33,327 to the power 21,110,688,929

33,327 to the power 337,015,929,936,783

33,327 to the power 41,233,629,897,003,167,041

33,327 to the power 541,113,183,577,424,547,975,407

First ten multiples33,327, 66,654, 99,981, 133,308, 166,635, 199,962, 233,289, 266,616, 299,943, 333,270

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 3

Divisible by 5No, remainder 2

Divisible by 6No, remainder 3

Divisible by 7Yes

Divisible by 8No, remainder 7

Divisible by 9Yes

Divisible by 10No, remainder 7

Divisible by 11No, remainder 8

Divisible by 12No, remainder 3

Divisible by 100No, remainder 27

Collatz (3n + 1) trajectory

Steps to reach 190the total stopping time

Highest value reached1,154,46434× the starting value

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

First steps33,327 → 99,982 → 49,991 → 149,974 → 74,987 → 224,962 → 112,481 → 337,444 → 168,722 → 84,361 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,332,700%

33,327% as a decimal333.27

33,327% of 10033,327

33,327% of 1,000333,270

As a fraction of 10033,327/100

Read another way

As seconds9 hours, 15 minutes and 27 seconds

As bytes32.546 KiB

As a 24-bit colour#00822F

Keep nerding

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