Recognised as Number
1,600,000
- Positive
- Even
- Composite
- 7 digits
1,600,000 is an even 7-digit integer and a composite number. It has 60 divisors and a digital root of 7.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value1,600,000
Digit count7
Digit sum7
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root7repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2^9 × 5^5
Distinct prime factors22, 5
Number of divisors60
Sum of divisors σ(n)3,995,838
Aliquot sum2,395,838sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)640,000integers below n that share no factor with it
Carmichael function λ(n)80,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 640,000
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, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1,000, 1,250, 1,280, 1,600, 2,000, 2,500, 2,560, 3,125, 3,200, 4,000, 5,000, 6,250, 6,400, 8,000, 10,000, 12,500, 12,800, 16,000, 20,000, 25,000, 32,000, 40,000, 50,000, 64,000, 80,000, 100,000, 160,000, 200,000, 320,000, 400,000, 800,000, 1,600,00060 in total
Arithmetic
Previous number1,599,999
Next number1,600,001
Double3,200,000
Half800,000
Square2,560,000,000,000
Cube4,096,000,000,000,000,000
Square root1,264.911064067≈irrational, shown to 9 decimal places
Cube root116.960709529≈
Negation-1,600,000
Reciprocal6.25 × 10^-7≈
Representations
Decimal1,600,000
Binary11000011010100000000021 bits
Octal6065000
Hexadecimal186A00
Base 36YAKG
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsone million, six hundred thousand
Ordinalone million, six hundred thousandth
Scientific notation1.6 × 10^6
Engineering notation1.6 × 10^6
In other bases
Ternary10000021210021base 3; the most digit-efficient integer base after e: 14 digits
Quinary402200000base 5; one hand: 9 digits
Septenary16412503base 7: 8 digits
Nonary3007707base 9; each digit is two ternary digits: 7 digits
Duodecimal651b14base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits
Vigesimala0000base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits
Sexagesimal7:24:26:40base 60; Babylonian, and still how an hour and a circle are divided: 4 digits
Balanced ternary1000010TT101T1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary11010011011111000000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000000000110000110101000000000
Bit length21 bitsto write the magnitude
Set bits6the population count, or Hamming weight
Zero bits15within that length
Bit parityeven6 set bits, so even; not the same as the number itself being even
Highest set bitbit 20worth 1,048,576
Lowest set bitbit 99 trailing zeros
Power of twoNo
Bytes318 6a 00
Gray code101000101111100000000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit00000000000110000110101000000000
64-bit0000000000000000000000000000000000000000000110000110101000000000
One's complement11111111111001111001010111111111at 32 bits, every bit flipped
Bits reversed00000000010101100001100000000000at 32 bits
Rotated left by 100000000001100001101010000000000at 32 bits, wrapping
Shifted left by 11100001101010000000000= 3,200,000, no wrap
Shifted right by 111000011010100000000= 800,000, discarding the low bit
These bits as a double7.90505033 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
1,600,000 to the power 22,560,000,000,000
1,600,000 to the power 34,096,000,000,000,000,000
1,600,000 to the power 46,553,600,000,000,000,000,000,000
1,600,000 to the power 510,485,760,000,000,000,000,000,000,000,000
First ten multiples1,600,000, 3,200,000, 4,800,000, 6,400,000, 8,000,000, 9,600,000, 11,200,000, 12,800,000, 14,400,000, 16,000,000
Powers of twoBetween 2^20 (1,048,576) and 2^21 (2,097,152)
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 3
Divisible by 8Yes
Divisible by 9No, remainder 7
Divisible by 10Yes
Divisible by 11No, remainder 6
Divisible by 12No, remainder 4
Divisible by 100Yes
Collatz (3n + 1) trajectory
Steps to reach 1132the total stopping time
Highest value reached1,600,000
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps1,600,000 → 800,000 → 400,000 → 200,000 → 100,000 → 50,000 → 25,000 → 12,500 → 6,250 → 3,125 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage160,000,000%
1,600,000% as a decimal16,000
1,600,000% of 1001,600,000
1,600,000% of 1,00016,000,000
As a fraction of 1001,600,000/100
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