Recognised as Number
18
- Positive
- Even
- Composite
- 2 digits
18 is an even 2-digit integer and a composite number. It has 6 divisors and a digital root of 9.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value18
Digit count2
Digit sum9
Digit product8
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root9repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2 × 3^2
Distinct prime factors22, 3
Number of divisors6
Sum of divisors σ(n)39
Aliquot sum21sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)6integers below n that share no factor with it
Carmichael function λ(n)6the smallest exponent with aˣ ≡ 1 for every unit coprime to n
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 6, 9, 186 in total
Arithmetic
Representations
Decimal18
Binary100105 bits
Octal22
Hexadecimal12
Base 36I
Roman numeralXVIII
In wordseighteen
Ordinaleighteenth
Scientific notation1.8 × 10^1
Engineering notation18
In other bases
Ternary200base 3; the most digit-efficient integer base after e: 3 digits
Quinary33base 5; one hand: 2 digits
Septenary24base 7: 2 digits
Nonary20base 9; each digit is two ternary digits: 2 digits
Duodecimal16base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits
Vigesimalibase 20; hands and feet, and the Mayan and Yoruba systems: 1 digit
Sexagesimal18base 60; Babylonian, and still how an hour and a circle are divided: 1 digit
Balanced ternary1T00digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary10110base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00010010
Bit length5 bitsto write the magnitude
Set bits2the population count, or Hamming weight
Zero bits3within that length
Bit parityeven2 set bits, so even; not the same as the number itself being even
Highest set bitbit 4worth 16
Lowest set bitbit 11 trailing zero
Power of twoNo
Bytes112
Gray code11011n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
8-bit00010010
16-bit0000000000010010
32-bit00000000000000000000000000010010
64-bit0000000000000000000000000000000000000000000000000000000000010010
One's complement11101101at 8 bits, every bit flipped
Bits reversed01001000at 8 bits
Rotated left by 100100100at 8 bits, wrapping
Shifted left by 1100100= 36, no wrap
Shifted right by 11001= 9, discarding the low bit
These bits as a double8.89318163 × 10^-323≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
18 to the power 2324
18 to the power 35,832
18 to the power 4104,976
18 to the power 51,889,568
First ten multiples18, 36, 54, 72, 90, 108, 126, 144, 162, 180
Powers of twoBetween 2^4 (16) and 2^5 (32)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4No, remainder 2
Divisible by 5No, remainder 3
Divisible by 6Yes
Divisible by 7No, remainder 4
Divisible by 8No, remainder 2
Divisible by 9Yes
Divisible by 10No, remainder 8
Divisible by 11No, remainder 7
Divisible by 12No, remainder 6
Divisible by 100No, remainder 18
Collatz (3n + 1) trajectory
Steps to reach 120the total stopping time
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps18 → 9 → 28 → 14 → 7 → 22 → 11 → 34 → 17 → 52 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage1,800%
18% as a decimal0.18
18% of 10018
18% of 1,000180
As a fraction of 10018/100
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