Recognised as Number
36
- Positive
- Even
- Composite
- Perfect square
- 2 digits
36 is an even 2-digit integer and a composite number. It has 9 divisors and a digital root of 9.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value36
Digit count2
Digit sum9
Digit product18
Multiplicative persistence2times the digit product can be taken before one digit is left
Digital root9repeated digit sum
PalindromicNoreads differently backwards
Perfect squareYes, 6²
Triangular numberYes, the 8th triangular number
Happy numberNosquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^2 × 3^2
Distinct prime factors22, 3
Number of divisors9
Sum of divisors σ(n)91
Aliquot sum55sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)12integers below n that share no factor with it
Carmichael function λ(n)6the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 12
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 6, 9, 12, 18, 369 in total
Arithmetic
Representations
Decimal36
Binary1001006 bits
Octal44
Hexadecimal24
Base 3610
Roman numeralXXXVI
In wordsthirty-six
Ordinalthirty-sixth
Scientific notation3.6 × 10^1
Engineering notation36
In other bases
Ternary1100base 3; the most digit-efficient integer base after e — 4 digits
Quinary121base 5; one hand — 3 digits
Septenary51base 7 — 2 digits
Nonary40base 9; each digit is two ternary digits — 2 digits
Duodecimal30base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves — 2 digits
Vigesimal1gbase 20; hands and feet, and the Mayan and Yoruba systems — 2 digits
Sexagesimal36base 60; Babylonian, and still how an hour and a circle are divided — 1 digit
Balanced ternary1100digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1100100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00100100
Bit length6 bitsto write the magnitude
Set bits2the population count, or Hamming weight
Zero bits4within that length
Bit parityeven2 set bits, so even; not the same as the number itself being even
Highest set bitbit 5worth 32
Lowest set bitbit 22 trailing zeros
Power of twoNo
Bytes124
Gray code110110n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
8-bit00100100
16-bit0000000000100100
32-bit00000000000000000000000000100100
64-bit0000000000000000000000000000000000000000000000000000000000100100
One's complement11011011at 8 bits, every bit flipped
Bits reversed00100100at 8 bits
Rotated left by 101001000at 8 bits, wrapping
Shifted left by 11001000= 72, no wrap
Shifted right by 110010= 18, discarding the low bit
These bits as a double1.77863633 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
36 to the power 21,296
36 to the power 346,656
36 to the power 41,679,616
36 to the power 560,466,176
First ten multiples36, 72, 108, 144, 180, 216, 252, 288, 324, 360
Powers of twoBetween 2^5 (32) and 2^6 (64)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5No, remainder 1
Divisible by 6Yes
Divisible by 7No, remainder 1
Divisible by 8No, remainder 4
Divisible by 9Yes
Divisible by 10No, remainder 6
Divisible by 11No, remainder 3
Divisible by 12Yes
Divisible by 100No, remainder 36
Collatz (3n + 1) trajectory
Steps to reach 121the total stopping time
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps36 → 18 → 9 → 28 → 14 → 7 → 22 → 11 → 34 → 17 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage3,600%
36% as a decimal0.36
36% of 10036
36% of 1,000360
As a fraction of 10036/100
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