Recognised as Number
88
- Positive
- Even
- Composite
- 2 digits
88 is an even 2-digit integer and a composite number. It has 8 divisors and a digital root of 7.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value88
Digit count2
Digit sum16
Digit product64
Multiplicative persistence3times the digit product can be taken before one digit is left
Digital root7repeated digit sum
PalindromicYesreads the same backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2^3 × 11
Distinct prime factors22, 11
Number of divisors8
Sum of divisors σ(n)180
Aliquot sum92sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)40integers below n that share no factor with it
Carmichael function λ(n)10the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 40
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 4, 8, 11, 22, 44, 888 in total
Arithmetic
Representations
Decimal88
Binary10110007 bits
Octal130
Hexadecimal58
Base 362G
Roman numeralLXXXVIII
In wordseighty-eight
Ordinaleighty-eighth
Scientific notation8.8 × 10^1
Engineering notation88
In other bases
Ternary10021base 3; the most digit-efficient integer base after e: 5 digits
Quinary323base 5; one hand: 3 digits
Septenary154base 7: 3 digits
Nonary107base 9; each digit is two ternary digits: 3 digits
Duodecimal74base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits
Vigesimal48base 20; hands and feet, and the Mayan and Yoruba systems: 2 digits
Sexagesimal1:28base 60; Babylonian, and still how an hour and a circle are divided: 2 digits
Balanced ternary101T1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary110101000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
01011000
Bit length7 bitsto write the magnitude
Set bits3the population count, or Hamming weight
Zero bits4within that length
Bit parityodd3 set bits, so odd; not the same as the number itself being even
Highest set bitbit 6worth 64
Lowest set bitbit 33 trailing zeros
Power of twoNo
Bytes158
Gray code1110100n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
8-bit01011000
16-bit0000000001011000
32-bit00000000000000000000000001011000
64-bit0000000000000000000000000000000000000000000000000000000001011000
One's complement10100111at 8 bits, every bit flipped
Bits reversed00011010at 8 bits
Rotated left by 110110000at 8 bits, wrapping
Shifted left by 110110000= 176, no wrap
Shifted right by 1101100= 44, discarding the low bit
These bits as a double4.34777768 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
88 to the power 27,744
88 to the power 3681,472
88 to the power 459,969,536
88 to the power 55,277,319,168
First ten multiples88, 176, 264, 352, 440, 528, 616, 704, 792, 880
Powers of twoBetween 2^6 (64) and 2^7 (128)
Divisibility tests
Divisible by 2Yes
Divisible by 3No, remainder 1
Divisible by 4Yes
Divisible by 5No, remainder 3
Divisible by 6No, remainder 4
Divisible by 7No, remainder 4
Divisible by 8Yes
Divisible by 9No, remainder 7
Divisible by 10No, remainder 8
Divisible by 11Yes
Divisible by 12No, remainder 4
Divisible by 100No, remainder 88
Collatz (3n + 1) trajectory
Steps to reach 117the total stopping time
Highest value reached88
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps88 → 44 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage8,800%
88% as a decimal0.88
88% of 10088
88% of 1,000880
As a fraction of 10088/100
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