Number

12,000

Positive
Even
Composite
5 digits

12,000 is an even 5-digit integer and a composite number. It has 48 divisors and a digital root of 3.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value12,000

Digit count5

Digit sum3

Digital root3repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^5 × 3 × 5^3

Distinct prime factors32, 3, 5

Number of divisors48

Sum of divisors σ(n)39,312

Aliquot sum27,312sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)3,200integers below n that share no factor with it

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 125, 150, 160, 200, 240, 250, 300, 375, 400, 480, 500, 600, 750, 800, 1,000, 1,200, 1,500, 2,000, 2,400, 3,000, 4,000, 6,000, 12,00048 in total

Arithmetic

Previous number11,999

Next number12,001

Double24,000

Half6,000

Square144,000,000

Cube1,728,000,000,000

Square root109.544511501≈irrational, shown to 9 decimal places

Cube root22.894284851≈

Negation-12,000

Reciprocal0.0000833333≈

Representations

Decimal12,000

Binary1011101110000014 bits

Octal27340

Hexadecimal2EE0

Base 3699C

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

In wordstwelve thousand

Ordinaltwelve thousandth

Scientific notation1.2 × 10^4

Engineering notation12 × 10^3

Nearest landmarks

Next prime12,007+7

Previous prime11,987−13

Distance to nearest prime7

Nearest square below11,881

Nearest square above12,100

Powers & multiples

12,000 to the power 2144,000,000

12,000 to the power 31,728,000,000,000

12,000 to the power 420,736,000,000,000,000

12,000 to the power 5248,832,000,000,000,000,000

First ten multiples12,000, 24,000, 36,000, 48,000, 60,000, 72,000, 84,000, 96,000, 108,000, 120,000

Powers of twoBetween 2^13 (8,192) and 2^14 (16,384)

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5Yes

Divisible by 6Yes

Divisible by 7No, remainder 2

Divisible by 8Yes

Divisible by 9No, remainder 3

Divisible by 10Yes

Divisible by 11No, remainder 10

Divisible by 12Yes

Divisible by 100Yes

Collatz (3n + 1) trajectory

Steps to reach 150the total stopping time

Highest value reached12,000

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

First steps12,000 → 6,000 → 3,000 → 1,500 → 750 → 375 → 1,126 → 563 → 1,690 → 845 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,200,000%

12,000% as a decimal120

12,000% of 10012,000

12,000% of 1,000120,000

As a fraction of 10012,000/100

Read another way

As seconds3 hours and 20 minutes

As bytes11.719 KiB

As a 24-bit colour#002EE0

Keep nerding

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