Recognised as Number

33,972

Positive
Even
Composite
5 digits

33,972 is an even 5-digit integer and a composite number. It has 24 divisors and a digital root of 6.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value33,972

Digit count5

Digit sum24

Digit product1,134

Multiplicative persistence3times 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 numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 3 × 19 × 149

Distinct prime factors42, 3, 19, 149

Number of divisors24

Sum of divisors σ(n)84,000

Aliquot sum50,028sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)10,656integers below n that share no factor with it

Carmichael function λ(n)1,332the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 10,656

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 149, 228, 298, 447, 596, 894, 1,788, 2,831, 5,662, 8,493, 11,324, 16,986, 33,97224 in total

Arithmetic

Previous number33,971

Next number33,973

Double67,944

Half16,986

Square1,154,096,784

Cube39,206,975,946,048

Square root184.314947847≈irrational, shown to 9 decimal places

Cube root32.387222518≈

Negation-33,972

Reciprocal0.000029436≈

Representations

Decimal33,972

Binary100001001011010016 bits

Octal102264

Hexadecimal84B4

Base 36Q7O

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

In wordsthirty-three thousand, nine hundred and seventy-two

Ordinalthirty-three thousand, nine hundred and seventy-second

Scientific notation3.3972 × 10^4

Engineering notation33.972 × 10^3

In other bases

Ternary1201121020base 3; the most digit-efficient integer base after e: 10 digits

Quinary2041342base 5; one hand: 7 digits

Septenary201021base 7: 6 digits

Nonary51536base 9; each digit is two ternary digits: 5 digits

Duodecimal177b0base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal44icbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:26:12base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT1TTT11T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000010111110100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000010010110100

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 b4

Gray code1100011011101110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000010010110100

32-bit00000000000000001000010010110100

64-bit0000000000000000000000000000000000000000000000001000010010110100

One's complement0111101101001011at 16 bits, every bit flipped

Bits reversed0010110100100001at 16 bits

Rotated left by 10000100101101001at 16 bits, wrapping

Shifted left by 110000100101101000= 67,944, no wrap

Shifted right by 1100001001011010= 16,986, discarding the low bit

These bits as a double1.67843981 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,997+25

Previous prime33,967−5

Distance to nearest prime5

Nearest square below33,856

Nearest square above34,225

Powers & multiples

33,972 to the power 21,154,096,784

33,972 to the power 339,206,975,946,048

33,972 to the power 41,331,939,386,839,142,656

33,972 to the power 545,248,644,849,699,354,309,632

First ten multiples33,972, 67,944, 101,916, 135,888, 169,860, 203,832, 237,804, 271,776, 305,748, 339,720

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 1

Divisible by 8No, remainder 4

Divisible by 9No, remainder 6

Divisible by 10No, remainder 2

Divisible by 11No, remainder 4

Divisible by 12Yes

Divisible by 100No, remainder 72

Collatz (3n + 1) trajectory

Steps to reach 136the total stopping time

Highest value reached33,972

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

First steps33,972 → 16,986 → 8,493 → 25,480 → 12,740 → 6,370 → 3,185 → 9,556 → 4,778 → 2,389 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,397,200%

33,972% as a decimal339.72

33,972% of 10033,972

33,972% of 1,000339,720

As a fraction of 10033,972/100

Read another way

As seconds9 hours, 26 minutes and 12 seconds

As bytes33.176 KiB

As a 24-bit colour#0084B4

Keep nerding

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