Recognised as Number
980,000,000,000,000,000
- Positive
- Even
- Composite
- 18 digits
980,000,000,000,000,000 is an even 18-digit integer and a composite number. It has 918 divisors and a digital root of 8.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value980,000,000,000,000,000
Digit count18
Digit sum17
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root8repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2^17 × 5^16 × 7^2
Distinct prime factors32, 5, 7
Number of divisors918
Sum of divisors σ(n)2,849,989,128,109,057,431
Aliquot sum1,869,989,128,109,057,431sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)336,000,000,000,000,000integers below n that share no factor with it
Carmichael function λ(n)21,000,000,000,000,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 336,000,000,000,000,000
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors918 divisors, too many to listlisting is capped at 512
Arithmetic
Previous number979,999,999,999,999,999
Next number980,000,000,000,000,001
Square960,400,000,000,000,000,000,000,000,000,000,000
Cube941,192,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Square root989,949,493≈irrational, shown to 9 decimal places
Cube root993,288≈
Negation-980,000,000,000,000,000
Representations
Decimal980,000,000,000,000,000
Binary11011001100110101000110011101100011111100010000000000000000060 bits
Octal66315214730770400000
HexadecimalD99A8CEC7E20000
Base 367G1H08U5TOU8
In wordsnine hundred and eighty quadrillion
Ordinalnine hundred and eighty quadrillionth
Engineering notation980 × 10^15
In other bases
Ternary20112021210112001000212201202001011022base 3; the most digit-efficient integer base after e: 38 digits
Quinary31210101030000000000000000base 5; one hand: 26 digits
Septenary1516545521331016543100base 7: 22 digits
Nonary6467715030781661138base 9; each digit is two ternary digits: 19 digits
Duodecimal5373563158a939768base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 17 digits
Vigesimalbj532a00000000base 20; hands and feet, and the Mayan and Yoruba systems: 14 digits
Sexagesimal1:37:14:40:1:5:50:37:2:13:20base 60; Babylonian, and still how an hour and a circle are divided: 11 digits
Balanced ternary1T1TTT10TT11TTT0010010T0T1TT1T00101110Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1001011101110111110011101001111011000001001100000000000000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0000110110011001101010001100111011000111111000100000000000000000
Bit length60 bitsto write the magnitude
Set bits24the population count, or Hamming weight
Zero bits36within that length
Bit parityeven24 set bits, so even; not the same as the number itself being even
Highest set bitbit 59worth 576,460,752,303,423,488
Lowest set bitbit 1717 trailing zeros
Power of twoNo
Bytes80d 99 a8 ce c7 e2 00 00
Gray code101101010101011111001010100110100100000100110000000000000000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
64-bit0000110110011001101010001100111011000111111000100000000000000000
One's complement1111001001100110010101110011000100111000000111011111111111111111at 64 bits, every bit flipped
Bits reversed0000000000000000010001111110001101110011000101011001100110110000at 64 bits
Rotated left by 10001101100110011010100011001110110001111110001000000000000000000at 64 bits, wrapping
Shifted left by 11101100110011010100011001110110001111110001000000000000000000= 1,960,000,000,000,000,000, no wrap
Shifted right by 111011001100110101000110011101100011111100010000000000000000= 490,000,000,000,000,000, discarding the low bit
These bits as a double3.75794221 × 10^-243≈IEEE-754 binary64 reinterpretation of the same 64 bits (normal)
Nearest landmarks
Distance to nearest prime9
Nearest square below979,999,998,690,957,049
Nearest square above980,000,000,670,856,036
Powers & multiples
980,000,000,000,000,000 to the power 2960,400,000,000,000,000,000,000,000,000,000,000
980,000,000,000,000,000 to the power 3941192000000000000000000000000… (54 digits)
980,000,000,000,000,000 to the power 4922368160000000000000000000000… (72 digits)
980,000,000,000,000,000 to the power 5903920796800000000000000000000… (90 digits)
First ten multiples980,000,000,000,000,000, 1,960,000,000,000,000,000, 2,940,000,000,000,000,000, 3,920,000,000,000,000,000, 4,900,000,000,000,000,000, 5,880,000,000,000,000,000, 6,860,000,000,000,000,000, 7,840,000,000,000,000,000, 8,820,000,000,000,000,000, 9,800,000,000,000,000,000
Powers of twoBetween 2^59 (576,460,752,303,423,488) and 2^60 (1,152,921,504,606,846,976)
Divisibility tests
Divisible by 2Yes
Divisible by 3No, remainder 2
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6No, remainder 2
Divisible by 7Yes
Divisible by 8Yes
Divisible by 9No, remainder 8
Divisible by 10Yes
Divisible by 11No, remainder 10
Divisible by 12No, remainder 8
Divisible by 100Yes
Collatz (3n + 1) trajectory
Steps to reach 1210the total stopping time
Highest value reached980,000,000,000,000,000
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps980,000,000,000,000,000 → 490,000,000,000,000,000 → 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 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
Keep nerding
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