Recognised as Number

27,002

Positive
Even
Composite
5 digits

27,002 is an even 5-digit integer and a composite number. It has 8 divisors and a digital root of 2.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value27,002

Digit count5

Digit sum11

Digit product0zero, because one of the digits is zero

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

Digital root2repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2 × 23 × 587

Distinct prime factors32, 23, 587

Number of divisors8

Sum of divisors σ(n)42,336

Aliquot sum15,334sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)12,892integers below n that share no factor with it

Carmichael function λ(n)6,446the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 12,892

Möbius function μ(n)−13 distinct prime factors, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 2, 23, 46, 587, 1,174, 13,501, 27,0028 in total

Arithmetic

Previous number27,001

Next number27,003

Double54,004

Half13,501

Square729,108,004

Cube19,687,374,324,008

Square root164.322852945≈irrational, shown to 9 decimal places

Cube root30.000740722≈

Negation-27,002

Reciprocal0.0000370343≈

Representations

Decimal27,002

Binary11010010111101015 bits

Octal64572

Hexadecimal697A

Base 36KU2

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

In wordstwenty-seven thousand and two

Ordinaltwenty-seven thousand and second

Scientific notation2.7002 × 10^4

Engineering notation27.002 × 10^3

In other bases

Ternary1101001002base 3; the most digit-efficient integer base after e: 10 digits

Quinary1331002base 5; one hand: 7 digits

Septenary141503base 7: 6 digits

Nonary41032base 9; each digit is two ternary digits: 5 digits

Duodecimal13762base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal37a2base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal7:30:2base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary110100101Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11011111010001110base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0110100101111010

Bit length15 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits6within that length

Bit parityodd9 set bits, so odd; not the same as the number itself being even

Highest set bitbit 14worth 16,384

Lowest set bitbit 11 trailing zero

Power of twoNo

Bytes269 7a

Gray code101110111000111n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0110100101111010

32-bit00000000000000000110100101111010

64-bit0000000000000000000000000000000000000000000000000110100101111010

One's complement1001011010000101at 16 bits, every bit flipped

Bits reversed0101111010010110at 16 bits

Rotated left by 11101001011110100at 16 bits, wrapping

Shifted left by 11101001011110100= 54,004, no wrap

Shifted right by 111010010111101= 13,501, discarding the low bit

These bits as a double1.33407606 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime27,011+9

Previous prime26,993−9

Distance to nearest prime9

Nearest square below26,896

Nearest square above27,225

Powers & multiples

27,002 to the power 2729,108,004

27,002 to the power 319,687,374,324,008

27,002 to the power 4531,598,481,496,864,016

27,002 to the power 514,354,222,197,378,322,160,032

First ten multiples27,002, 54,004, 81,006, 108,008, 135,010, 162,012, 189,014, 216,016, 243,018, 270,020

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

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 2

Divisible by 4No, remainder 2

Divisible by 5No, remainder 2

Divisible by 6No, remainder 2

Divisible by 7No, remainder 3

Divisible by 8No, remainder 2

Divisible by 9No, remainder 2

Divisible by 10No, remainder 2

Divisible by 11No, remainder 8

Divisible by 12No, remainder 2

Divisible by 100No, remainder 2

Collatz (3n + 1) trajectory

Steps to reach 1139the total stopping time

Highest value reached40,5041× the starting value

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

First steps27,002 → 13,501 → 40,504 → 20,252 → 10,126 → 5,063 → 15,190 → 7,595 → 22,786 → 11,393 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage2,700,200%

27,002% as a decimal270.02

27,002% of 10027,002

27,002% of 1,000270,020

As a fraction of 10027,002/100

Read another way

As seconds7 hours, 30 minutes and 2 seconds

As bytes26.369 KiB

As a 24-bit colour#00697A

Keep nerding

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