Recognised as Number
6,000,000
- Positive
- Even
- Composite
- 7 digits
6,000,000 is an even 7-digit integer and a composite number. It has 112 divisors and a digital root of 6.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value6,000,000
Digit count7
Digit sum6
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root6repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^7 × 3 × 5^6
Distinct prime factors32, 3, 5
Number of divisors112
Sum of divisors σ(n)19,921,620
Aliquot sum13,921,620sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)1,600,000integers below n that share no factor with it
Carmichael function λ(n)100,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 1,600,000
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 125, 128, 150, 160, 192, 200, 240, 250, 300, 320, 375, 384, 400, 480, 500, 600, 625, 640, 750, 800, 960, 1,000, 1,200, 1,250, 1,500, 1,600, 1,875, 1,920, 2,000, 2,400, 2,500, 3,000, 3,125, 3,200, 3,750, 4,000, 4,800, 5,000, 6,000, 6,250, 7,500, 8,000, 9,375, 9,600, 10,000, 12,000, 12,500, 15,000, 15,625, 16,000, 18,750, 20,000, 24,000, 25,000, 30,000, 31,250, 37,500, 40,000, 46,875, 48,000, 50,000, 60,000, 62,500, 75,000, 80,000, 93,750, 100,000, 120,000, 125,000, 150,000, 187,500, 200,000, 240,000, 250,000, 300,000, 375,000, 400,000, 500,000, 600,000, 750,000, 1,000,000, 1,200,000, 1,500,000, 2,000,000, 3,000,000, 6,000,000112 in total
Arithmetic
Previous number5,999,999
Next number6,000,001
Double12,000,000
Half3,000,000
Square36,000,000,000,000
Cube216,000,000,000,000,000,000
Square root2,449.489742783≈irrational, shown to 9 decimal places
Cube root181.712059283≈
Negation-6,000,000
Reciprocal1.66666667 × 10^-7≈
Representations
Decimal6,000,000
Binary1011011100011011000000023 bits
Octal26706600
Hexadecimal5B8D80
Base 363KLMO
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordssix million
Ordinalsix millionth
Scientific notation6 × 10^6
Engineering notation6 × 10^6
In other bases
Ternary102021211110020base 3; the most digit-efficient integer base after e: 15 digits
Quinary3014000000base 5; one hand: 10 digits
Septenary101666466base 7: 9 digits
Nonary12254406base 9; each digit is two ternary digits: 8 digits
Duodecimal2014280base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 7 digits
Vigesimal1ha000base 20; hands and feet, and the Mayan and Yoruba systems: 6 digits
Sexagesimal27:46:40:0base 60; Babylonian, and still how an hour and a circle are divided: 4 digits
Balanced ternary11T10TT111101T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1101011001001001010000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000000010110111000110110000000
Bit length23 bitsto write the magnitude
Set bits10the population count, or Hamming weight
Zero bits13within that length
Bit parityeven10 set bits, so even; not the same as the number itself being even
Highest set bitbit 22worth 4,194,304
Lowest set bitbit 77 trailing zeros
Power of twoNo
Bytes35b 8d 80
Gray code11101100100101101000000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit00000000010110111000110110000000
64-bit0000000000000000000000000000000000000000010110111000110110000000
One's complement11111111101001000111001001111111at 32 bits, every bit flipped
Bits reversed00000001101100011101101000000000at 32 bits
Rotated left by 100000000101101110001101100000000at 32 bits, wrapping
Shifted left by 1101101110001101100000000= 12,000,000, no wrap
Shifted right by 11011011100011011000000= 3,000,000, discarding the low bit
These bits as a double2.96439388 × 10^-317≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
6,000,000 to the power 236,000,000,000,000
6,000,000 to the power 3216,000,000,000,000,000,000
6,000,000 to the power 41,296,000,000,000,000,000,000,000,000
6,000,000 to the power 57,776,000,000,000,000,000,000,000,000,000,000
First ten multiples6,000,000, 12,000,000, 18,000,000, 24,000,000, 30,000,000, 36,000,000, 42,000,000, 48,000,000, 54,000,000, 60,000,000
Powers of twoBetween 2^22 (4,194,304) and 2^23 (8,388,608)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6Yes
Divisible by 7No, remainder 6
Divisible by 8Yes
Divisible by 9No, remainder 6
Divisible by 10Yes
Divisible by 11No, remainder 6
Divisible by 12Yes
Divisible by 100Yes
Collatz (3n + 1) trajectory
Steps to reach 1113the total stopping time
Highest value reached6,000,000
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps6,000,000 → 3,000,000 → 1,500,000 → 750,000 → 375,000 → 187,500 → 93,750 → 46,875 → 140,626 → 70,313 → …
Last steps… → 32 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage600,000,000%
6,000,000% as a decimal60,000
6,000,000% of 1006,000,000
6,000,000% of 1,00060,000,000
As a fraction of 1006,000,000/100
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