Recognised as Number
56
- Positive
- Even
- Composite
- 2 digits
56 is an even 2-digit integer and a composite number. It has 8 divisors and a digital root of 2.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value56
Digit count2
Digit sum11
Digit product30
Multiplicative persistence2times the digit product can be taken before one digit is left
Digital root2repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2^3 × 7
Distinct prime factors22, 7
Number of divisors8
Sum of divisors σ(n)120
Aliquot sum64sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)24integers 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) = 24
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 4, 7, 8, 14, 28, 568 in total
Arithmetic
Representations
Decimal56
Binary1110006 bits
Octal70
Hexadecimal38
Base 361K
Roman numeralLVI
In wordsfifty-six
Ordinalfifty-sixth
Scientific notation5.6 × 10^1
Engineering notation56
In other bases
Ternary2002base 3; the most digit-efficient integer base after e: 4 digits
Quinary211base 5; one hand: 3 digits
Septenary110base 7: 3 digits
Nonary62base 9; each digit is two ternary digits: 2 digits
Duodecimal48base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits
Vigesimal2gbase 20; hands and feet, and the Mayan and Yoruba systems: 2 digits
Sexagesimal56base 60; Babylonian, and still how an hour and a circle are divided: 1 digit
Balanced ternary1T01Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1001000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00111000
Bit length6 bitsto write the magnitude
Set bits3the population count, or Hamming weight
Zero bits3within that length
Bit parityodd3 set bits, so odd; not the same as the number itself being even
Highest set bitbit 5worth 32
Lowest set bitbit 33 trailing zeros
Power of twoNo
Bytes138
Gray code100100n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
8-bit00111000
16-bit0000000000111000
32-bit00000000000000000000000000111000
64-bit0000000000000000000000000000000000000000000000000000000000111000
One's complement11000111at 8 bits, every bit flipped
Bits reversed00011100at 8 bits
Rotated left by 101110000at 8 bits, wrapping
Shifted left by 11110000= 112, no wrap
Shifted right by 111100= 28, discarding the low bit
These bits as a double2.76676762 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
56 to the power 23,136
56 to the power 3175,616
56 to the power 49,834,496
56 to the power 5550,731,776
First ten multiples56, 112, 168, 224, 280, 336, 392, 448, 504, 560
Powers of twoBetween 2^5 (32) and 2^6 (64)
Divisibility tests
Divisible by 2Yes
Divisible by 3No, remainder 2
Divisible by 4Yes
Divisible by 5No, remainder 1
Divisible by 6No, remainder 2
Divisible by 7Yes
Divisible by 8Yes
Divisible by 9No, remainder 2
Divisible by 10No, remainder 6
Divisible by 11No, remainder 1
Divisible by 12No, remainder 8
Divisible by 100No, remainder 56
Collatz (3n + 1) trajectory
Steps to reach 119the total stopping time
Highest value reached56
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps56 → 28 → 14 → 7 → 22 → 11 → 34 → 17 → 52 → 26 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage5,600%
56% as a decimal0.56
56% of 10056
56% of 1,000560
As a fraction of 10056/100
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