Recognised as Number

1,116,002

Positive
Even
Composite
7 digits

1,116,002 is an even 7-digit integer and a composite number. It has 8 divisors and a digital root of 2.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value1,116,002

Digit count7

Digit sum11

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 factorisation2 × 137 × 4,073

Distinct prime factors32, 137, 4,073

Number of divisors8

Sum of divisors σ(n)1,686,636

Aliquot sum570,634sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)553,792integers below n that share no factor with it

Carmichael function λ(n)69,224the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 553,792

Möbius function μ(n)−13 distinct prime factors, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 2, 137, 274, 4,073, 8,146, 558,001, 1,116,0028 in total

Arithmetic

Previous number1,116,001

Next number1,116,003

Double2,232,004

Half558,001

Square1,245,460,464,004

Cube1,389,936,368,749,392,008

Square root1,056.409958302≈irrational, shown to 9 decimal places

Cube root103.726165716≈

Negation-1,116,002

Reciprocal8.96055742 × 10^-7≈

Representations

Decimal1,116,002

Binary10001000001110110001021 bits

Octal4203542

Hexadecimal110762

Base 36NX42

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

In wordsone million, one hundred and sixteen thousand and two

Ordinalone million, one hundred and sixteen thousand and second

Scientific notation1.116002 × 10^6

Engineering notation1.116002 × 10^6

In other bases

Ternary2002200212102base 3; the most digit-efficient integer base after e: 13 digits

Quinary241203002base 5; one hand: 9 digits

Septenary12325436base 7: 8 digits

Nonary2080772base 9; each digit is two ternary digits: 7 digits

Duodecimal459a02base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimal6ja02base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal5:10:0:2base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary1T010T010TT11Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100010001100010100110base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000100010000011101100010

Bit length21 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits13within that length

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

Highest set bitbit 20worth 1,048,576

Lowest set bitbit 11 trailing zero

Power of twoNo

Bytes311 07 62

Gray code110011000010011010011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000100010000011101100010

64-bit0000000000000000000000000000000000000000000100010000011101100010

One's complement11111111111011101111100010011101at 32 bits, every bit flipped

Bits reversed01000110111000001000100000000000at 32 bits

Rotated left by 100000000001000100000111011000100at 32 bits, wrapping

Shifted left by 11000100000111011000100= 2,232,004, no wrap

Shifted right by 110001000001110110001= 558,001, discarding the low bit

These bits as a double5.51378249 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,116,053+51

Previous prime1,116,001−1

Distance to nearest prime1

Nearest square below1,115,136

Nearest square above1,117,249

Powers & multiples

1,116,002 to the power 21,245,460,464,004

1,116,002 to the power 31,389,936,368,749,392,008

1,116,002 to the power 41,551,171,767,397,058,979,712,016

1,116,002 to the power 51,731,110,794,758,652,615,476,569,280,032

First ten multiples1,116,002, 2,232,004, 3,348,006, 4,464,008, 5,580,010, 6,696,012, 7,812,014, 8,928,016, 10,044,018, 11,160,020

Powers of twoBetween 2^20 (1,048,576) and 2^21 (2,097,152)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 2

Divisible by 4No, remainder 2

Divisible by 5No, remainder 2

Divisible by 6No, remainder 2

Divisible by 7No, remainder 6

Divisible by 8No, remainder 2

Divisible by 9No, remainder 2

Divisible by 10No, remainder 2

Divisible by 11No, remainder 8

Divisible by 12No, remainder 2

Divisible by 100No, remainder 2

Collatz (3n + 1) trajectory

Steps to reach 1116the total stopping time

Highest value reached1,674,0041× the starting value

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

First steps1,116,002 → 558,001 → 1,674,004 → 837,002 → 418,501 → 1,255,504 → 627,752 → 313,876 → 156,938 → 78,469 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage111,600,200%

1,116,002% as a decimal11,160.02

1,116,002% of 1001,116,002

1,116,002% of 1,00011,160,020

As a fraction of 1001,116,002/100

Read another way

As seconds12 days, 22 hours and 2 seconds

As bytes1.064 MiB

As a 24-bit colour#110762

Keep nerding

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