Recognised as Number
24
- Positive
- Even
- Composite
- 2 digits
24 is an even 2-digit integer and a composite number. It has 8 divisors and a digital root of 6.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value24
Digit count2
Digit sum6
Digit product8
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root6repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^3 × 3
Distinct prime factors22, 3
Number of divisors8
Sum of divisors σ(n)60
Aliquot sum36sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)8integers below n that share no factor with it
Carmichael function λ(n)2the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 8
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 6, 8, 12, 248 in total
Arithmetic
Representations
Decimal24
Binary110005 bits
Octal30
Hexadecimal18
Base 36O
Roman numeralXXIV
In wordstwenty-four
Ordinaltwenty-fourth
Scientific notation2.4 × 10^1
Engineering notation24
In other bases
Ternary220base 3; the most digit-efficient integer base after e: 3 digits
Quinary44base 5; one hand: 2 digits
Septenary33base 7: 2 digits
Nonary26base 9; each digit is two ternary digits: 2 digits
Duodecimal20base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits
Vigesimal14base 20; hands and feet, and the Mayan and Yoruba systems: 2 digits
Sexagesimal24base 60; Babylonian, and still how an hour and a circle are divided: 1 digit
Balanced ternary10T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1101000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00011000
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 33 trailing zeros
Power of twoNo
Bytes118
Gray code10100n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
8-bit00011000
16-bit0000000000011000
32-bit00000000000000000000000000011000
64-bit0000000000000000000000000000000000000000000000000000000000011000
One's complement11100111at 8 bits, every bit flipped
Bits reversed00011000at 8 bits
Rotated left by 100110000at 8 bits, wrapping
Shifted left by 1110000= 48, no wrap
Shifted right by 11100= 12, discarding the low bit
These bits as a double1.18575755 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
24 to the power 2576
24 to the power 313,824
24 to the power 4331,776
24 to the power 57,962,624
First ten multiples24, 48, 72, 96, 120, 144, 168, 192, 216, 240
Powers of twoBetween 2^4 (16) and 2^5 (32)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5No, remainder 4
Divisible by 6Yes
Divisible by 7No, remainder 3
Divisible by 8Yes
Divisible by 9No, remainder 6
Divisible by 10No, remainder 4
Divisible by 11No, remainder 2
Divisible by 12Yes
Divisible by 100No, remainder 24
Collatz (3n + 1) trajectory
Steps to reach 110the total stopping time
Highest value reached24
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps24 → 12 → 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage2,400%
24% as a decimal0.24
24% of 10024
24% of 1,000240
As a fraction of 10024/100
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