Recognised as Number

343,000,000,000,000,000,000

Positive
Even
Composite
Perfect cube
21 digits

343,000,000,000,000,000,000 is an even 21-digit integer and a composite number. It has 1,444 divisors and a digital root of 1.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value343,000,000,000,000,000,000

Digit count21

Digit sum10

Digit product0zero, because one of the digits is zero

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

Digital root1repeated digit sum

PalindromicNoreads differently backwards

Perfect cubeYes, 7,000,000³

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^18 × 5^18 × 7^3

Distinct prime factors32, 5, 7

Number of divisors1,444

Sum of divisors σ(n)999,998,092,651,314,758,800

Aliquot sum656,998,092,651,314,758,800sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)117,600,000,000,000,000,000integers below n that share no factor with it

Carmichael function λ(n)7,350,000,000,000,000,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 117,600,000,000,000,000,000

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

SquarefreeNohas a repeated prime factor

All divisors1,444 divisors, too many to listlisting is capped at 512

Arithmetic

Previous number342,999,999,999,999,999,999

Next number343,000,000,000,000,000,001

Double686,000,000,000,000,000,000

Square117,649,000,000,000,000,000,000,000,000,000,000,000,000

Cube40,353,607,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Square root18,520,259,177≈irrational, shown to 9 decimal places

Cube root7,000,000

Negation-343,000,000,000,000,000,000

Representations

Decimal343,000,000,000,000,000,000

Binary10010100110000001010011001010101101010100011011111100000000000000000069 bits

Octal45140246253250677000000

Hexadecimal129814CAB546FC0000

Base 3620DYBCDX8MNHTS

In wordsthree hundred and forty-three quintillion

Ordinalthree hundred and forty-three quintillionth

Engineering notation343 × 10^18

In other bases

Ternary10010122020001221222101101121220211000200201base 3; the most digit-efficient integer base after e: 44 digits

Quinary141004243032000000000000000000base 5; one hand: 30 digits

Septenary1535044306544330041531000base 7: 25 digits

Nonary3118201858341556730621base 9; each digit is two ternary digits: 22 digits

Duodecimal10a726b07115638aa454base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 20 digits

Vigesimala9704df000000000base 20; hands and feet, and the Mayan and Yoruba systems: 16 digits

Sexagesimal9:27:15:33:26:24:5:16:2:57:46:40base 60; Babylonian, and still how an hour and a circle are divided: 12 digits

Balanced ternary10011T0T1T001T00T00T10111TT0T0T1T11001T01T01digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary101111110100000010101110111111111010101011011000011000000000000000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

Bit length69 bitsto write the magnitude

Set bits25the population count, or Hamming weight

Zero bits44within that length

Bit parityodd25 set bits, so odd; not the same as the number itself being even

Highest set bitbit 68worth 295,147,905,179,352,825,856

Lowest set bitbit 1818 trailing zeros

Power of twoNo

Bytes912 98 14 ca b5 46 fc 00 00

Gray code110111101010000011110101011111110111111100101100000100000000000000000n XOR (n >> 1); successive values differ in exactly one bit

Nearest landmarks

Next prime343,000,000,000,000,000,003+3

Previous prime342,999,999,999,999,999,991−9

Distance to nearest prime3

Nearest square below342,999,999,983,252,717,329

Nearest square above343,000,000,020,293,235,684

Powers & multiples

343,000,000,000,000,000,000 to the power 2117649000000000000000000000000… (42 digits)

343,000,000,000,000,000,000 to the power 3403536070000000000000000000000… (62 digits)

343,000,000,000,000,000,000 to the power 4138412872010000000000000000000… (83 digits)

343,000,000,000,000,000,000 to the power 5474756150994300000000000000000… (103 digits)

First ten multiples343,000,000,000,000,000,000, 686,000,000,000,000,000,000, 1,029,000,000,000,000,000,000, 1,372,000,000,000,000,000,000, 1,715,000,000,000,000,000,000, 2,058,000,000,000,000,000,000, 2,401,000,000,000,000,000,000, 2,744,000,000,000,000,000,000, 3,087,000,000,000,000,000,000, 3,430,000,000,000,000,000,000

Powers of twoBetween 2^68 (295,147,905,179,352,825,856) and 2^69 (590,295,810,358,705,651,712)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 1

Divisible by 4Yes

Divisible by 5Yes

Divisible by 6No, remainder 4

Divisible by 7Yes

Divisible by 8Yes

Divisible by 9No, remainder 1

Divisible by 10Yes

Divisible by 11No, remainder 2

Divisible by 12No, remainder 4

Divisible by 100Yes

Collatz (3n + 1) trajectory

Steps to reach 1296the total stopping time

Highest value reached343,000,000,000,000,000,000

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

First steps343,000,000,000,000,000,000 → 171,500,000,000,000,000,000 → 85,750,000,000,000,000,000 → 42,875,000,000,000,000,000 → 21,437,500,000,000,000,000 → 10,718,750,000,000,000,000 → 5,359,375,000,000,000,000 → 2,679,687,500,000,000,000 → 1,339,843,750,000,000,000 → 669,921,875,000,000,000 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

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