Recognised as Number
22
- Positive
- Even
- Composite
- 2 digits
22 is an even 2-digit integer and a composite number. It has 4 divisors and a digital root of 4.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value22
Digit count2
Digit sum4
Digit product4
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root4repeated digit sum
PalindromicYesreads the same backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2 × 11
Distinct prime factors22, 11
Number of divisors4
Sum of divisors σ(n)36
Aliquot sum14sum of the proper divisors
ClassificationDeficientthe aliquot sum is less than the number
Euler's totient φ(n)10integers below n that share no factor with it
Carmichael function λ(n)10the smallest exponent with aˣ ≡ 1 for every unit coprime to n
Möbius function μ(n)+12 distinct prime factors, an even number of them
SquarefreeYesno repeated prime factor
All divisors1, 2, 11, 224 in total
Arithmetic
Representations
Decimal22
Binary101105 bits
Octal26
Hexadecimal16
Base 36M
Roman numeralXXII
In wordstwenty-two
Ordinaltwenty-second
Scientific notation2.2 × 10^1
Engineering notation22
In other bases
Ternary211base 3; the most digit-efficient integer base after e: 3 digits
Quinary42base 5; one hand: 2 digits
Septenary31base 7: 2 digits
Nonary24base 9; each digit is two ternary digits: 2 digits
Duodecimal1abase 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits
Vigesimal12base 20; hands and feet, and the Mayan and Yoruba systems: 2 digits
Sexagesimal22base 60; Babylonian, and still how an hour and a circle are divided: 1 digit
Balanced ternary1T11digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1101010base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00010110
Bit length5 bitsto write the magnitude
Set bits3the population count, or Hamming weight
Zero bits2within that length
Bit parityodd3 set bits, so odd; not the same as the number itself being even
Highest set bitbit 4worth 16
Lowest set bitbit 11 trailing zero
Power of twoNo
Bytes116
Gray code11101n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
8-bit00010110
16-bit0000000000010110
32-bit00000000000000000000000000010110
64-bit0000000000000000000000000000000000000000000000000000000000010110
One's complement11101001at 8 bits, every bit flipped
Bits reversed01101000at 8 bits
Rotated left by 100101100at 8 bits, wrapping
Shifted left by 1101100= 44, no wrap
Shifted right by 11011= 11, discarding the low bit
These bits as a double1.08694442 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
22 to the power 2484
22 to the power 310,648
22 to the power 4234,256
22 to the power 55,153,632
First ten multiples22, 44, 66, 88, 110, 132, 154, 176, 198, 220
Powers of twoBetween 2^4 (16) and 2^5 (32)
Divisibility tests
Divisible by 2Yes
Divisible by 3No, remainder 1
Divisible by 4No, remainder 2
Divisible by 5No, remainder 2
Divisible by 6No, remainder 4
Divisible by 7No, remainder 1
Divisible by 8No, remainder 6
Divisible by 9No, remainder 4
Divisible by 10No, remainder 2
Divisible by 11Yes
Divisible by 12No, remainder 10
Divisible by 100No, remainder 22
Collatz (3n + 1) trajectory
Steps to reach 115the total stopping time
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage2,200%
22% as a decimal0.22
22% of 10022
22% of 1,000220
As a fraction of 10022/100
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