Recognised as Number

33,732

Positive
Even
Composite
5 digits

33,732 is an even 5-digit integer and a composite number. It has 18 divisors and a digital root of 9.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value33,732

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 numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 3^2 × 937

Distinct prime factors32, 3, 937

Number of divisors18

Sum of divisors σ(n)85,358

Aliquot sum51,626sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)11,232integers below n that share no factor with it

Carmichael function λ(n)936the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 11,232

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 9, 12, 18, 36, 937, 1,874, 2,811, 3,748, 5,622, 8,433, 11,244, 16,866, 33,73218 in total

Arithmetic

Previous number33,731

Next number33,733

Double67,464

Half16,866

Square1,137,847,824

Cube38,381,882,799,168

Square root183.66273438≈irrational, shown to 9 decimal places

Cube root32.31077417≈

Negation-33,732

Reciprocal0.0000296454≈

Representations

Decimal33,732

Binary100000111100010016 bits

Octal101704

Hexadecimal83C4

Base 36Q10

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

In wordsthirty-three thousand, seven hundred and thirty-two

Ordinalthirty-three thousand, seven hundred and thirty-second

Scientific notation3.3732 × 10^4

Engineering notation33.732 × 10^3

In other bases

Ternary1201021100base 3; the most digit-efficient integer base after e: 10 digits

Quinary2034412base 5; one hand: 7 digits

Septenary200226base 7: 6 digits

Nonary51240base 9; each digit is two ternary digits: 5 digits

Duodecimal17630base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal446cbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:22:12base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT011T1100digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000010011000100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000001111000100

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

Bytes283 c4

Gray code1100001000100110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000001111000100

32-bit00000000000000001000001111000100

64-bit0000000000000000000000000000000000000000000000001000001111000100

One's complement0111110000111011at 16 bits, every bit flipped

Bits reversed0010001111000001at 16 bits

Rotated left by 10000011110001001at 16 bits, wrapping

Shifted left by 110000011110001000= 67,464, no wrap

Shifted right by 1100000111100010= 16,866, discarding the low bit

These bits as a double1.66658224 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,739+7

Previous prime33,721−11

Distance to nearest prime7

Nearest square below33,489

Nearest square above33,856

Powers & multiples

33,732 to the power 21,137,847,824

33,732 to the power 338,381,882,799,168

33,732 to the power 41,294,697,670,581,534,976

33,732 to the power 543,672,741,824,056,337,810,432

First ten multiples33,732, 67,464, 101,196, 134,928, 168,660, 202,392, 236,124, 269,856, 303,588, 337,320

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 2

Divisible by 6Yes

Divisible by 7No, remainder 6

Divisible by 8No, remainder 4

Divisible by 9Yes

Divisible by 10No, remainder 2

Divisible by 11No, remainder 6

Divisible by 12Yes

Divisible by 100No, remainder 32

Collatz (3n + 1) trajectory

Steps to reach 185the total stopping time

Highest value reached33,732

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

First steps33,732 → 16,866 → 8,433 → 25,300 → 12,650 → 6,325 → 18,976 → 9,488 → 4,744 → 2,372 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,373,200%

33,732% as a decimal337.32

33,732% of 10033,732

33,732% of 1,000337,320

As a fraction of 10033,732/100

Read another way

As seconds9 hours, 22 minutes and 12 seconds

As bytes32.941 KiB

As a 24-bit colour#0083C4

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