Recognised as Number

10,000,000,000,000,000,000,000

Positive
Even
Composite
Perfect square
23 digits

10,000,000,000,000,000,000,000 is an even 23-digit integer and a composite number. It has 529 divisors and a digital root of 1.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value10,000,000,000,000,000,000,000

Digit count23

Digit sum1

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 squareYes, 100,000,000,000²

Happy numberYessquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^22 × 5^22

Distinct prime factors22, 5

Number of divisors529

Sum of divisors σ(n)24,999,997,019,767,759,133,317

Aliquot sum14,999,997,019,767,759,133,317sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)4,000,000,000,000,000,000,000integers below n that share no factor with it

Carmichael function λ(n)500,000,000,000,000,000,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 4,000,000,000,000,000,000,000

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

SquarefreeNohas a repeated prime factor

All divisors529 divisors, too many to listlisting is capped at 512

Arithmetic

Previous number9,999,999,999,999,999,999,999

Next number10,000,000,000,000,000,000,001

Double20,000,000,000,000,000,000,000

Square100,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Cube1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Square root100,000,000,000exact

Cube root21,544,346≈

Negation-10,000,000,000,000,000,000,000

Representations

Decimal10,000,000,000,000,000,000,000

Binary1000011110000110011110000011001001101110101011001001000000000000000000000074 bits

Octal2074147406233526220000000

Hexadecimal21E19E0C9BAB2400000

Base 361MMFB877TU0O6PS

In wordsten sextillion

Ordinalten sextillionth

Engineering notation10 × 10^21

In other bases

Ternary10101101120122002111101201110222020110022221101base 3; the most digit-efficient integer base after e: 47 digits

Quinary20332042040000000000000000000000base 5; one hand: 32 digits

Septenary103124430006141042330114154base 7: 27 digits

Nonary111346562441643866408841base 9; each digit is two ternary digits: 24 digits

Duodecimal27373a86ba1a194a65054base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 21 digits

Vigesimalf53a6500000000000base 20; hands and feet, and the Mayan and Yoruba systems: 17 digits

Sexagesimal4:35:38:10:18:4:35:26:44:56:17:46:40base 60; Babylonian, and still how an hour and a circle are divided: 13 digits

Balanced ternary1010111TTT1T0T01T11111TT0111100T1T01101000T1101digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary110011000100110111000100001110111101100111111110110010000000000000000000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

Bit length74 bitsto write the magnitude

Set bits25the population count, or Hamming weight

Zero bits49within that length

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

Highest set bitbit 73worth 9,444,732,965,739,290,427,392

Lowest set bitbit 2222 trailing zeros

Power of twoNo

Bytes1002 1e 19 e0 c9 ba b2 40 00 00

Gray code11000100010001010100010000101011010110011111101011011000000000000000000000n XOR (n >> 1); successive values differ in exactly one bit

Nearest landmarks

Next prime10,000,000,000,000,000,000,009+9

Previous prime9,999,999,999,999,999,999,973−27

Distance to nearest prime9

Nearest square below10,000,000,000,000,000,000,000

Nearest square above10,000,000,000,200,000,000,001

Powers & multiples

10,000,000,000,000,000,000,000 to the power 2100000000000000000000000000000… (45 digits)

10,000,000,000,000,000,000,000 to the power 3100000000000000000000000000000… (67 digits)

10,000,000,000,000,000,000,000 to the power 4100000000000000000000000000000… (89 digits)

10,000,000,000,000,000,000,000 to the power 5100000000000000000000000000000… (111 digits)

First ten multiples10,000,000,000,000,000,000,000, 20,000,000,000,000,000,000,000, 30,000,000,000,000,000,000,000, 40,000,000,000,000,000,000,000, 50,000,000,000,000,000,000,000, 60,000,000,000,000,000,000,000, 70,000,000,000,000,000,000,000, 80,000,000,000,000,000,000,000, 90,000,000,000,000,000,000,000, 100,000,000,000,000,000,000,000

Powers of twoBetween 2^73 (9,444,732,965,739,290,427,392) and 2^74 (18,889,465,931,478,580,854,784)

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 4

Divisible by 8Yes

Divisible by 9No, remainder 1

Divisible by 10Yes

Divisible by 11No, remainder 1

Divisible by 12No, remainder 4

Divisible by 100Yes

Collatz (3n + 1) trajectory

Steps to reach 1324the total stopping time

Highest value reached10,000,000,000,000,000,000,000

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

First steps10,000,000,000,000,000,000,000 → 5,000,000,000,000,000,000,000 → 2,500,000,000,000,000,000,000 → 1,250,000,000,000,000,000,000 → 625,000,000,000,000,000,000 → 312,500,000,000,000,000,000 → 156,250,000,000,000,000,000 → 78,125,000,000,000,000,000 → 39,062,500,000,000,000,000 → 19,531,250,000,000,000,000 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

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