Recognised as Number

8,440,013

Positive
Odd
Composite
7 digits

8,440,013 is an odd 7-digit integer and a composite number. It has 4 divisors and a digital root of 2.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value8,440,013

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 factorisation167 × 50,539

Distinct prime factors2167, 50,539

Number of divisors4

Sum of divisors σ(n)8,490,720

Aliquot sum50,707sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)8,389,308integers below n that share no factor with it

Carmichael function λ(n)4,194,654the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 8,389,308

Möbius function μ(n)+12 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 167, 50,539, 8,440,0134 in total

Arithmetic

Previous number8,440,012

Next number8,440,014

Double16,880,026

Half4,220,006.5

Square71,233,819,440,169

Cube601,214,362,114,679,082,197

Square root2,905.170046658≈irrational, shown to 9 decimal places

Cube root203.601530591≈

Negation-8,440,013

Reciprocal1.1848323 × 10^-7≈

Representations

Decimal8,440,013

Binary10000000110010001100110124 bits

Octal40144315

Hexadecimal80C8CD

Base 3650WCT

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

In wordseight million, four hundred and forty thousand and thirteen

Ordinaleight million, four hundred and forty thousand and thirteenth

Scientific notation8.440013 × 10^6

Engineering notation8.440013 × 10^6

In other bases

Ternary120212210112002base 3; the most digit-efficient integer base after e: 15 digits

Quinary4130040023base 5; one hand: 10 digits

Septenary131511311base 7: 9 digits

Nonary16783462base 9; each digit is two ternary digits: 8 digits

Duodecimal29b0325base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 7 digits

Vigesimal2cf00dbase 20; hands and feet, and the Mayan and Yoruba systems: 6 digits

Sexagesimal39:4:26:53base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary1TT10T0T11TTT01Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary1100000011101100111011101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000100000001100100011001101

Bit length24 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits15within that length

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

Highest set bitbit 23worth 8,388,608

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes380 c8 cd

Gray code110000001010110010101011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000100000001100100011001101

64-bit0000000000000000000000000000000000000000100000001100100011001101

One's complement11111111011111110011011100110010at 32 bits, every bit flipped

Bits reversed10110011000100110000000100000000at 32 bits

Rotated left by 100000001000000011001000110011010at 32 bits, wrapping

Shifted left by 11000000011001000110011010= 16,880,026, no wrap

Shifted right by 110000000110010001100110= 4,220,006, discarding the low bit

These bits as a double4.16992047 × 10^-317≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime8,440,031+18

Previous prime8,439,989−24

Distance to nearest prime18

Nearest square below8,439,025

Nearest square above8,444,836

Powers & multiples

8,440,013 to the power 271,233,819,440,169

8,440,013 to the power 3601,214,362,114,679,082,197

8,440,013 to the power 45,074,257,032,034,598,944,570,748,561

8,440,013 to the power 542,826,795,315,713,431,541,963,397,274,571,293

First ten multiples8,440,013, 16,880,026, 25,320,039, 33,760,052, 42,200,065, 50,640,078, 59,080,091, 67,520,104, 75,960,117, 84,400,130

Powers of twoBetween 2^23 (8,388,608) and 2^24 (16,777,216)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 3

Divisible by 6No, remainder 5

Divisible by 7No, remainder 1

Divisible by 8No, remainder 5

Divisible by 9No, remainder 2

Divisible by 10No, remainder 3

Divisible by 11No, remainder 10

Divisible by 12No, remainder 5

Divisible by 100No, remainder 13

Collatz (3n + 1) trajectory

Steps to reach 1106the total stopping time

Highest value reached25,320,0403× the starting value

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

First steps8,440,013 → 25,320,040 → 12,660,020 → 6,330,010 → 3,165,005 → 9,495,016 → 4,747,508 → 2,373,754 → 1,186,877 → 3,560,632 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage844,001,300%

8,440,013% as a decimal84,400.13

8,440,013% of 1008,440,013

8,440,013% of 1,00084,400,130

As a fraction of 1008,440,013/100

Read another way

As seconds97 days, 16 hours and 26 minutes

As bytes8.049 MiB

As a 24-bit colour#80C8CD

Keep nerding

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