Recognised as Number

1,040,080

Positive
Even
Composite
7 digits

1,040,080 is an even 7-digit integer and a composite number. It has 20 divisors and a digital root of 4.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value1,040,080

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 factorisation2^4 × 5 × 13,001

Distinct prime factors32, 5, 13,001

Number of divisors20

Sum of divisors σ(n)2,418,372

Aliquot sum1,378,292sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)416,000integers below n that share no factor with it

Carmichael function λ(n)13,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 416,000

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 13,001, 26,002, 52,004, 65,005, 104,008, 130,010, 208,016, 260,020, 520,040, 1,040,08020 in total

Arithmetic

Previous number1,040,079

Next number1,040,081

Double2,080,160

Half520,040

Square1,081,766,406,400

Cube1,125,123,603,968,512,000

Square root1,019.843125191≈irrational, shown to 9 decimal places

Cube root101.31853816≈

Negation-1,040,080

Reciprocal9.61464503 × 10^-7≈

Representations

Decimal1,040,080

Binary1111110111101101000020 bits

Octal3757320

HexadecimalFDED0

Base 36MAJ4

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

In wordsone million, forty thousand and eighty

Ordinalone million, forty thousand and eightieth

Scientific notation1.04008 × 10^6

Engineering notation1.04008 × 10^6

In other bases

Ternary1221211201111base 3; the most digit-efficient integer base after e: 13 digits

Quinary231240310base 5; one hand: 9 digits

Septenary11561206base 7: 8 digits

Nonary1854644base 9; each digit is two ternary digits: 7 digits

Duodecimal421a94base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimal6a040base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal4:48:54:40base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary1T00T0TTT01111digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100000010001111010000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000011111101111011010000

Bit length20 bitsto write the magnitude

Set bits13the population count, or Hamming weight

Zero bits7within that length

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

Highest set bitbit 19worth 524,288

Lowest set bitbit 44 trailing zeros

Power of twoNo

Bytes30f de d0

Gray code10000011000110111000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000011111101111011010000

64-bit0000000000000000000000000000000000000000000011111101111011010000

One's complement11111111111100000010000100101111at 32 bits, every bit flipped

Bits reversed00001011011110111111000000000000at 32 bits

Rotated left by 100000000000111111011110110100000at 32 bits, wrapping

Shifted left by 1111111011110110100000= 2,080,160, no wrap

Shifted right by 11111110111101101000= 520,040, discarding the low bit

These bits as a double5.13867797 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,040,089+9

Previous prime1,040,071−9

Distance to nearest prime9

Nearest square below1,038,361

Nearest square above1,040,400

Powers & multiples

1,040,080 to the power 21,081,766,406,400

1,040,080 to the power 31,125,123,603,968,512,000

1,040,080 to the power 41,170,218,558,015,569,960,960,000

1,040,080 to the power 51,217,120,917,820,834,004,995,276,800,000

First ten multiples1,040,080, 2,080,160, 3,120,240, 4,160,320, 5,200,400, 6,240,480, 7,280,560, 8,320,640, 9,360,720, 10,400,800

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 6

Divisible by 8Yes

Divisible by 9No, remainder 4

Divisible by 10Yes

Divisible by 11No, remainder 8

Divisible by 12No, remainder 4

Divisible by 100No, remainder 80

Collatz (3n + 1) trajectory

Steps to reach 1103the total stopping time

Highest value reached1,040,080

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

First steps1,040,080 → 520,040 → 260,020 → 130,010 → 65,005 → 195,016 → 97,508 → 48,754 → 24,377 → 73,132 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage104,008,000%

1,040,080% as a decimal10,400.8

1,040,080% of 1001,040,080

1,040,080% of 1,00010,400,800

As a fraction of 1001,040,080/100

Read another way

As seconds12 days, 54 minutes and 40 seconds

As bytes1,015.703 KiB

As a 24-bit colour#0FDED0

Keep nerding

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