Recognised as Number

2,009,009

Positive
Odd
Composite
7 digits

2,009,009 is an odd 7-digit integer and a composite number. It has 8 divisors and a digital root of 2.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value2,009,009

Digit count7

Digit sum20

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 factorisation17 × 59 × 2,003

Distinct prime factors317, 59, 2,003

Number of divisors8

Sum of divisors σ(n)2,164,320

Aliquot sum155,311sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)1,857,856integers below n that share no factor with it

Carmichael function λ(n)464,464the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 1,857,856

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

SquarefreeYesno repeated prime factor

All divisors1, 17, 59, 1,003, 2,003, 34,051, 118,177, 2,009,0098 in total

Arithmetic

Previous number2,009,008

Next number2,009,010

Double4,018,018

Half1,004,504.5

Square4,036,117,162,081

Cube8,108,595,703,675,187,729

Square root1,417.395146034≈irrational, shown to 9 decimal places

Cube root126.180998794≈

Negation-2,009,009

Reciprocal4.9775785 × 10^-7≈

Representations

Decimal2,009,009

Binary11110101001111011000121 bits

Octal7523661

Hexadecimal1EA7B1

Base 361725T

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

In wordstwo million, nine thousand and nine

Ordinaltwo million, nine thousand and ninth

Scientific notation2.009009 × 10^6

Engineering notation2.009009 × 10^6

In other bases

Ternary10210001211202base 3; the most digit-efficient integer base after e: 14 digits

Quinary1003242014base 5; one hand: 10 digits

Septenary23035112base 7: 8 digits

Nonary3701752base 9; each digit is two ternary digits: 7 digits

Duodecimal80a755base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimalcb2a9base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal9:18:3:29base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary11T1001T0TTT1Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000111111100011110001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000111101010011110110001

Bit length21 bitsto write the magnitude

Set bits13the population count, or Hamming weight

Zero bits8within that length

Bit parityodd13 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 20worth 1,048,576

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes31e a7 b1

Gray code100011111010001101001n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000111101010011110110001

64-bit0000000000000000000000000000000000000000000111101010011110110001

One's complement11111111111000010101100001001110at 32 bits, every bit flipped

Bits reversed10001101111001010111100000000000at 32 bits

Rotated left by 100000000001111010100111101100010at 32 bits, wrapping

Shifted left by 11111010100111101100010= 4,018,018, no wrap

Shifted right by 111110101001111011000= 1,004,504, discarding the low bit

These bits as a double9.92582329 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime2,009,011+2

Previous prime2,008,973−36

Distance to nearest prime2

Nearest square below2,007,889

Nearest square above2,010,724

Powers & multiples

2,009,009 to the power 24,036,117,162,081

2,009,009 to the power 38,108,595,703,675,187,729

2,009,009 to the power 416,290,241,746,044,785,224,250,561

2,009,009 to the power 532,727,242,279,979,687,918,586,395,304,049

First ten multiples2,009,009, 4,018,018, 6,027,027, 8,036,036, 10,045,045, 12,054,054, 14,063,063, 16,072,072, 18,081,081, 20,090,090

Powers of twoBetween 2^20 (1,048,576) and 2^21 (2,097,152)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 4

Divisible by 6No, remainder 5

Divisible by 7No, remainder 2

Divisible by 8No, remainder 1

Divisible by 9No, remainder 2

Divisible by 10No, remainder 9

Divisible by 11No, remainder 2

Divisible by 12No, remainder 5

Divisible by 100No, remainder 9

Collatz (3n + 1) trajectory

Steps to reach 1135the total stopping time

Highest value reached6,027,0283× the starting value

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

First steps2,009,009 → 6,027,028 → 3,013,514 → 1,506,757 → 4,520,272 → 2,260,136 → 1,130,068 → 565,034 → 282,517 → 847,552 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage200,900,900%

2,009,009% as a decimal20,090.09

2,009,009% of 1002,009,009

2,009,009% of 1,00020,090,090

As a fraction of 1002,009,009/100

Read another way

As seconds23 days, 6 hours and 3 minutes

As bytes1.916 MiB

As a 24-bit colour#1EA7B1

Keep nerding

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