Recognised as Number

21,210

Positive
Even
Composite
5 digits

21,210 is an even 5-digit integer and a composite number. It has 32 divisors and a digital root of 6.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value21,210

Digit count5

Digit sum6

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 numberYessquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2 × 3 × 5 × 7 × 101

Distinct prime factors52, 3, 5, 7, 101

Number of divisors32

Sum of divisors σ(n)58,752

Aliquot sum37,542sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)4,800integers below n that share no factor with it

Carmichael function λ(n)300the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 4,800

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

SquarefreeYesno repeated prime factor

All divisors1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 101, 105, 202, 210, 303, 505, 606, 707, 1,010, 1,414, 1,515, 2,121, 3,030, 3,535, 4,242, 7,070, 10,605, 21,21032 in total

Arithmetic

Previous number21,209

Next number21,211

Double42,420

Half10,605

Square449,864,100

Cube9,541,617,561,000

Square root145.636533878≈irrational, shown to 9 decimal places

Cube root27.680901048≈

Negation-21,210

Reciprocal0.0000471476≈

Representations

Decimal21,210

Binary10100101101101015 bits

Octal51332

Hexadecimal52DA

Base 36GD6

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

In wordstwenty-one thousand, two hundred and ten

Ordinaltwenty-one thousand, two hundred and tenth

Scientific notation2.121 × 10^4

Engineering notation21.21 × 10^3

In other bases

Ternary1002002120base 3; the most digit-efficient integer base after e: 10 digits

Quinary1134320base 5; one hand: 7 digits

Septenary115560base 7: 6 digits

Nonary32076base 9; each digit is two ternary digits: 5 digits

Duodecimal10336base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal2d0abase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal5:53:30base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary101T010TT0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary101011100101110base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0101001011011010

Bit length15 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits7within that length

Bit parityeven8 set bits, so even; not the same as the number itself being even

Highest set bitbit 14worth 16,384

Lowest set bitbit 11 trailing zero

Power of twoNo

Bytes252 da

Gray code111101110110111n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0101001011011010

32-bit00000000000000000101001011011010

64-bit0000000000000000000000000000000000000000000000000101001011011010

One's complement1010110100100101at 16 bits, every bit flipped

Bits reversed0101101101001010at 16 bits

Rotated left by 11010010110110100at 16 bits, wrapping

Shifted left by 11010010110110100= 42,420, no wrap

Shifted right by 110100101101101= 10,605, discarding the low bit

These bits as a double1.04791323 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime21,211+1

Previous prime21,193−17

Distance to nearest prime1

Nearest square below21,025

Nearest square above21,316

Powers & multiples

21,210 to the power 2449,864,100

21,210 to the power 39,541,617,561,000

21,210 to the power 4202,377,708,468,810,000

21,210 to the power 54,292,431,196,623,460,100,000

First ten multiples21,210, 42,420, 63,630, 84,840, 106,050, 127,260, 148,470, 169,680, 190,890, 212,100

Powers of twoBetween 2^14 (16,384) and 2^15 (32,768)

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4No, remainder 2

Divisible by 5Yes

Divisible by 6Yes

Divisible by 7Yes

Divisible by 8No, remainder 2

Divisible by 9No, remainder 6

Divisible by 10Yes

Divisible by 11No, remainder 2

Divisible by 12No, remainder 6

Divisible by 100No, remainder 10

Collatz (3n + 1) trajectory

Steps to reach 1149the total stopping time

Highest value reached31,8161× the starting value

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

First steps21,210 → 10,605 → 31,816 → 15,908 → 7,954 → 3,977 → 11,932 → 5,966 → 2,983 → 8,950 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,121,000%

21,210% as a decimal212.1

21,210% of 10021,210

21,210% of 1,000212,100

As a fraction of 10021,210/100

Read another way

As seconds5 hours, 53 minutes and 30 seconds

As bytes20.713 KiB

As a 24-bit colour#0052DA

Keep nerding

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