Recognised as Number

1,008,040

Positive
Even
Composite
7 digits

1,008,040 is an even 7-digit integer and a composite number. It has 64 divisors and a digital root of 4.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value1,008,040

Digit count7

Digit sum13

Digit product0zero, because one of the digits is zero

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

Digital root4repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^3 × 5 × 11 × 29 × 79

Distinct prime factors52, 5, 11, 29, 79

Number of divisors64

Sum of divisors σ(n)2,592,000

Aliquot sum1,583,960sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)349,440integers below n that share no factor with it

Carmichael function λ(n)5,460the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 349,440

Möbius function μ(n)0zero, because a prime divides n twice

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 5, 8, 10, 11, 20, 22, 29, 40, 44, 55, 58, 79, 88, 110, 116, 145, 158, 220, 232, 290, 316, 319, 395, 440, 580, 632, 638, 790, 869, 1,160, 1,276, 1,580, 1,595, 1,738, 2,291, 2,552, 3,160, 3,190, 3,476, 4,345, 4,582, 6,380, 6,952, 8,690, 9,164, 11,455, 12,760, 17,380, 18,328, 22,910, 25,201, 34,760, 45,820, 50,402, 91,640, 100,804, 126,005, 201,608, 252,010, 504,020, 1,008,04064 in total

Arithmetic

Previous number1,008,039

Next number1,008,041

Double2,016,080

Half504,020

Square1,016,144,641,600

Cube1,024,314,444,518,464,000

Square root1,004.01195212≈irrational, shown to 9 decimal places

Cube root100.267284951≈

Negation-1,008,040

Reciprocal9.92024126 × 10^-7≈

Representations

Decimal1,008,040

Binary1111011000011010100020 bits

Octal3660650

HexadecimalF61A8

Base 36LLT4

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

In wordsone million, eight thousand and forty

Ordinalone million, eight thousand and fortieth

Scientific notation1.00804 × 10^6

Engineering notation1.00804 × 10^6

In other bases

Ternary1220012202211base 3; the most digit-efficient integer base after e: 13 digits

Quinary224224130base 5; one hand: 9 digits

Septenary11365615base 7: 8 digits

Nonary1805684base 9; each digit is two ternary digits: 7 digits

Duodecimal407434base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimal66020base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal4:40:0:40base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary1T0T01T0T10T11digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100001010011011111000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000011110110000110101000

Bit length20 bitsto write the magnitude

Set bits10the population count, or Hamming weight

Zero bits10within that length

Bit parityeven10 set bits, so even; not the same as the number itself being even

Highest set bitbit 19worth 524,288

Lowest set bitbit 33 trailing zeros

Power of twoNo

Bytes30f 61 a8

Gray code10001101000101111100n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000011110110000110101000

64-bit0000000000000000000000000000000000000000000011110110000110101000

One's complement11111111111100001001111001010111at 32 bits, every bit flipped

Bits reversed00010101100001101111000000000000at 32 bits

Rotated left by 100000000000111101100001101010000at 32 bits, wrapping

Shifted left by 1111101100001101010000= 2,016,080, no wrap

Shifted right by 11111011000011010100= 504,020, discarding the low bit

These bits as a double4.98037934 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,008,041+1

Previous prime1,008,037−3

Distance to nearest prime1

Nearest square below1,008,016

Nearest square above1,010,025

Powers & multiples

1,008,040 to the power 21,016,144,641,600

1,008,040 to the power 31,024,314,444,518,464,000

1,008,040 to the power 41,032,549,932,652,392,450,560,000

1,008,040 to the power 51,040,851,634,110,917,685,862,502,400,000

First ten multiples1,008,040, 2,016,080, 3,024,120, 4,032,160, 5,040,200, 6,048,240, 7,056,280, 8,064,320, 9,072,360, 10,080,400

Powers of twoBetween 2^19 (524,288) and 2^20 (1,048,576)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 1

Divisible by 4Yes

Divisible by 5Yes

Divisible by 6No, remainder 4

Divisible by 7No, remainder 5

Divisible by 8Yes

Divisible by 9No, remainder 4

Divisible by 10Yes

Divisible by 11Yes

Divisible by 12No, remainder 4

Divisible by 100No, remainder 40

Collatz (3n + 1) trajectory

Steps to reach 1134the total stopping time

Highest value reached1,008,040

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

First steps1,008,040 → 504,020 → 252,010 → 126,005 → 378,016 → 189,008 → 94,504 → 47,252 → 23,626 → 11,813 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage100,804,000%

1,008,040% as a decimal10,080.4

1,008,040% of 1001,008,040

1,008,040% of 1,00010,080,400

As a fraction of 1001,008,040/100

Read another way

As seconds11 days, 16 hours and 40 seconds

As bytes984.414 KiB

As a 24-bit colour#0F61A8

Keep nerding

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