Recognised as Number

33,670

Positive
Even
Composite
5 digits

33,670 is an even 5-digit integer and a composite number. It has 32 divisors and a digital root of 1.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value33,670

Digit count5

Digit sum19

Digit product0zero, because one of the digits is zero

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

Digital root1repeated digit sum

PalindromicNoreads differently backwards

Triangular numberYes, the 259th triangular number

Happy numberYessquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2 × 5 × 7 × 13 × 37

Distinct prime factors52, 5, 7, 13, 37

Number of divisors32

Sum of divisors σ(n)76,608

Aliquot sum42,938sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)10,368integers below n that share no factor with it

Carmichael function λ(n)36the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 10,368

Möbius function μ(n)−15 distinct prime factors, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 2, 5, 7, 10, 13, 14, 26, 35, 37, 65, 70, 74, 91, 130, 182, 185, 259, 370, 455, 481, 518, 910, 962, 1,295, 2,405, 2,590, 3,367, 4,810, 6,734, 16,835, 33,67032 in total

Arithmetic

Previous number33,669

Next number33,671

Double67,340

Half16,835

Square1,133,668,900

Cube38,170,631,863,000

Square root183.493869107≈irrational, shown to 9 decimal places

Cube root32.290966108≈

Negation-33,670

Reciprocal0.0000297≈

Representations

Decimal33,670

Binary100000111000011016 bits

Octal101606

Hexadecimal8386

Base 36PZA

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

In wordsthirty-three thousand, six hundred and seventy

Ordinalthirty-three thousand, six hundred and seventieth

Scientific notation3.367 × 10^4

Engineering notation33.67 × 10^3

In other bases

Ternary1201012001base 3; the most digit-efficient integer base after e: 10 digits

Quinary2034140base 5; one hand: 7 digits

Septenary200110base 7: 6 digits

Nonary51161base 9; each digit is two ternary digits: 5 digits

Duodecimal1759abase 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal443abase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:21:10base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT011TT001digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000010010011010base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000001110000110

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 11 trailing zero

Power of twoNo

Bytes283 86

Gray code1100001001000101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000001110000110

32-bit00000000000000001000001110000110

64-bit0000000000000000000000000000000000000000000000001000001110000110

One's complement0111110001111001at 16 bits, every bit flipped

Bits reversed0110000111000001at 16 bits

Rotated left by 10000011100001101at 16 bits, wrapping

Shifted left by 110000011100001100= 67,340, no wrap

Shifted right by 1100000111000011= 16,835, discarding the low bit

These bits as a double1.66351903 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,679+9

Previous prime33,647−23

Distance to nearest prime9

Nearest square below33,489

Nearest square above33,856

Powers & multiples

33,670 to the power 21,133,668,900

33,670 to the power 338,170,631,863,000

33,670 to the power 41,285,205,174,827,210,000

33,670 to the power 543,272,858,236,432,160,700,000

First ten multiples33,670, 67,340, 101,010, 134,680, 168,350, 202,020, 235,690, 269,360, 303,030, 336,700

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

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 1

Divisible by 4No, remainder 2

Divisible by 5Yes

Divisible by 6No, remainder 4

Divisible by 7Yes

Divisible by 8No, remainder 6

Divisible by 9No, remainder 1

Divisible by 10Yes

Divisible by 11No, remainder 10

Divisible by 12No, remainder 10

Divisible by 100No, remainder 70

Collatz (3n + 1) trajectory

Steps to reach 1160the total stopping time

Highest value reached182,0685× the starting value

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

First steps33,670 → 16,835 → 50,506 → 25,253 → 75,760 → 37,880 → 18,940 → 9,470 → 4,735 → 14,206 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,367,000%

33,670% as a decimal336.7

33,670% of 10033,670

33,670% of 1,000336,700

As a fraction of 10033,670/100

Read another way

As seconds9 hours, 21 minutes and 10 seconds

As bytes32.881 KiB

As a 24-bit colour#008386

Keep nerding

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