Recognised as Number
490,000,000,000,000,000
- Positive
- Even
- Composite
- Perfect square
- 18 digits
490,000,000,000,000,000 is an even 18-digit integer and a composite number. It has 867 divisors and a digital root of 4.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value490,000,000,000,000,000
Digit count18
Digit sum13
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root4repeated digit sum
PalindromicNoreads differently backwards
Perfect squareYes, 700,000,000²
Happy numberYessquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2^16 × 5^16 × 7^2
Distinct prime factors32, 5, 7
Number of divisors867
Sum of divisors σ(n)1,424,989,128,110,925,207
Aliquot sum934,989,128,110,925,207sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)168,000,000,000,000,000integers below n that share no factor with it
Carmichael function λ(n)10,500,000,000,000,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 168,000,000,000,000,000
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors867 divisors, too many to listlisting is capped at 512
Arithmetic
Previous number489,999,999,999,999,999
Next number490,000,000,000,000,001
Double980,000,000,000,000,000
Square240,100,000,000,000,000,000,000,000,000,000,000
Cube117,649,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Square root700,000,000exact
Cube root788,373≈
Negation-490,000,000,000,000,000
Representations
Decimal490,000,000,000,000,000
Binary1101100110011010100011001110110001111110001000000000000000059 bits
Octal33146506354374200000
Hexadecimal6CCD46763F10000
Base 363Q0QI4F2WUF4
In wordsfour hundred and ninety quadrillion
Ordinalfour hundred and ninety quadrillionth
Engineering notation490 × 10^15
In other bases
Ternary10021010220021000111221100212112002011base 3; the most digit-efficient integer base after e: 38 digits
Quinary13102300240000000000000000base 5; one hand: 26 digits
Septenary606622610514006621400base 7: 21 digits
Nonary3233807014840775064base 9; each digit is two ternary digits: 19 digits
Duodecimal279789168a547a994base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 17 digits
Vigesimal5jcbb500000000base 20; hands and feet, and the Mayan and Yoruba systems: 14 digits
Sexagesimal48:37:20:0:32:55:18:31:6:40base 60; Babylonian, and still how an hour and a circle are divided: 10 digits
Balanced ternary101T10110T01T1001TTT0T11010T0TTT01T011digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1101111011101110101011011100010100100001100010000000000000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0000011011001100110101000110011101100011111100010000000000000000
Bit length59 bitsto write the magnitude
Set bits24the population count, or Hamming weight
Zero bits35within that length
Bit parityeven24 set bits, so even; not the same as the number itself being even
Highest set bitbit 58worth 288,230,376,151,711,744
Lowest set bitbit 1616 trailing zeros
Power of twoNo
Bytes806 cc d4 67 63 f1 00 00
Gray code10110101010101111100101010011010010000010011000000000000000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
64-bit0000011011001100110101000110011101100011111100010000000000000000
One's complement1111100100110011001010111001100010011100000011101111111111111111at 64 bits, every bit flipped
Bits reversed0000000000000000100011111100011011100110001010110011001101100000at 64 bits
Rotated left by 10000110110011001101010001100111011000111111000100000000000000000at 64 bits, wrapping
Shifted left by 1110110011001101010001100111011000111111000100000000000000000= 980,000,000,000,000,000, no wrap
Shifted right by 11101100110011010100011001110110001111110001000000000000000= 245,000,000,000,000,000, discarding the low bit
These bits as a double6.50540213 × 10^-276≈IEEE-754 binary64 reinterpretation of the same 64 bits (normal)
Nearest landmarks
Distance to nearest prime3
Nearest square below490,000,000,000,000,000
Nearest square above490,000,001,400,000,001
Powers & multiples
490,000,000,000,000,000 to the power 2240,100,000,000,000,000,000,000,000,000,000,000
490,000,000,000,000,000 to the power 3117649000000000000000000000000… (54 digits)
490,000,000,000,000,000 to the power 4576480100000000000000000000000… (71 digits)
490,000,000,000,000,000 to the power 5282475249000000000000000000000… (89 digits)
First ten multiples490,000,000,000,000,000, 980,000,000,000,000,000, 1,470,000,000,000,000,000, 1,960,000,000,000,000,000, 2,450,000,000,000,000,000, 2,940,000,000,000,000,000, 3,430,000,000,000,000,000, 3,920,000,000,000,000,000, 4,410,000,000,000,000,000, 4,900,000,000,000,000,000
Powers of twoBetween 2^58 (288,230,376,151,711,744) and 2^59 (576,460,752,303,423,488)
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 4
Divisible by 10Yes
Divisible by 11No, remainder 5
Divisible by 12No, remainder 4
Divisible by 100Yes
Collatz (3n + 1) trajectory
Steps to reach 1209the total stopping time
Highest value reached490,000,000,000,000,000
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps490,000,000,000,000,000 → 245,000,000,000,000,000 → 122,500,000,000,000,000 → 61,250,000,000,000,000 → 30,625,000,000,000,000 → 15,312,500,000,000,000 → 7,656,250,000,000,000 → 3,828,125,000,000,000 → 1,914,062,500,000,000 → 957,031,250,000,000 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
Keep nerding
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