Recognised as Number

1,000,128

Positive
Even
Composite
7 digits

1,000,128 is an even 7-digit integer and a composite number. It has 28 divisors and a digital root of 3.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value1,000,128

Digit count7

Digit sum12

Digit product0zero, because one of the digits is zero

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

Digital root3repeated digit sum

PalindromicNoreads differently backwards

Happy numberYessquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^6 × 3 × 5,209

Distinct prime factors32, 3, 5,209

Number of divisors28

Sum of divisors σ(n)2,646,680

Aliquot sum1,646,552sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)333,312integers below n that share no factor with it

Carmichael function λ(n)10,416the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 333,312

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 5,209, 10,418, 15,627, 20,836, 31,254, 41,672, 62,508, 83,344, 125,016, 166,688, 250,032, 333,376, 500,064, 1,000,12828 in total

Arithmetic

Previous number1,000,127

Next number1,000,129

Double2,000,256

Half500,064

Square1,000,256,016,384

Cube1,000,384,049,154,097,152

Square root1,000.063997952≈irrational, shown to 9 decimal places

Cube root100.004266485≈

Negation-1,000,128

Reciprocal9.99872016 × 10^-7≈

Representations

Decimal1,000,128

Binary1111010000101100000020 bits

Octal3641300

HexadecimalF42C0

Base 36LFPC

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

In wordsone million, one hundred and twenty-eight

Ordinalone million, one hundred and twenty-eighth

Scientific notation1.000128 × 10^6

Engineering notation1.000128 × 10^6

In other bases

Ternary1212210220210base 3; the most digit-efficient integer base after e: 13 digits

Quinary224001003base 5; one hand: 9 digits

Septenary11333553base 7: 8 digits

Nonary1783823base 9; each digit is two ternary digits: 7 digits

Duodecimal402940base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimal65068base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal4:37:48:48base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary1T0T0T110T1T10digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100110100011111000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000011110100001011000000

Bit length20 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits12within that length

Bit parityeven8 set bits, so even; not the same as the number itself being even

Highest set bitbit 19worth 524,288

Lowest set bitbit 66 trailing zeros

Power of twoNo

Bytes30f 42 c0

Gray code10001110001110100000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000011110100001011000000

64-bit0000000000000000000000000000000000000000000011110100001011000000

One's complement11111111111100001011110100111111at 32 bits, every bit flipped

Bits reversed00000011010000101111000000000000at 32 bits

Rotated left by 100000000000111101000010110000000at 32 bits, wrapping

Shifted left by 1111101000010110000000= 2,000,256, no wrap

Shifted right by 11111010000101100000= 500,064, discarding the low bit

These bits as a double4.94128886 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,000,133+5

Previous prime1,000,121−7

Distance to nearest prime5

Nearest square below1,000,000

Nearest square above1,002,001

Powers & multiples

1,000,128 to the power 21,000,256,016,384

1,000,128 to the power 31,000,384,049,154,097,152

1,000,128 to the power 41,000,512,098,312,388,876,435,456

1,000,128 to the power 51,000,640,163,860,972,862,211,639,738,368

First ten multiples1,000,128, 2,000,256, 3,000,384, 4,000,512, 5,000,640, 6,000,768, 7,000,896, 8,001,024, 9,001,152, 10,001,280

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

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5No, remainder 3

Divisible by 6Yes

Divisible by 7No, remainder 3

Divisible by 8Yes

Divisible by 9No, remainder 3

Divisible by 10No, remainder 8

Divisible by 11No, remainder 8

Divisible by 12Yes

Divisible by 100No, remainder 28

Collatz (3n + 1) trajectory

Steps to reach 1139the total stopping time

Highest value reached1,000,128

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

First steps1,000,128 → 500,064 → 250,032 → 125,016 → 62,508 → 31,254 → 15,627 → 46,882 → 23,441 → 70,324 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage100,012,800%

1,000,128% as a decimal10,001.28

1,000,128% of 1001,000,128

1,000,128% of 1,00010,001,280

As a fraction of 1001,000,128/100

Read another way

As seconds11 days, 13 hours and 48 minutes

As bytes976.688 KiB

As a 24-bit colour#0F42C0

Keep nerding

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