Recognised as Number

52

Positive
Even
Composite
2 digits

52 is an even 2-digit integer and a composite number. It has 6 divisors and a digital root of 7.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value52

Digit count2

Digit sum7

Digit product10

Multiplicative persistence2times the digit product can be taken before one digit is left

Digital root7repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 13

Distinct prime factors22, 13

Number of divisors6

Sum of divisors σ(n)98

Aliquot sum46sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)24integers below n that share no factor with it

Carmichael function λ(n)12the 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, 13, 26, 526 in total

Arithmetic

Previous number51

Next number53

Double104

Half26

Square2,704

Cube140,608

Square root7.211102551≈irrational, shown to 9 decimal places

Cube root3.732511157≈

Negation-52

Reciprocal0.0192307692≈

52 factorial8065817517094387857166063685640376697528… (68 digits)

Representations

Decimal52

Binary1101006 bits

Octal64

Hexadecimal34

Base 361G

Roman numeralLII

In wordsfifty-two

Ordinalfifty-second

Scientific notation5.2 × 10^1

Engineering notation52

In other bases

Ternary1221base 3; the most digit-efficient integer base after e: 4 digits

Quinary202base 5; one hand: 3 digits

Septenary103base 7: 3 digits

Nonary57base 9; each digit is two ternary digits: 2 digits

Duodecimal44base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits

Vigesimal2cbase 20; hands and feet, and the Mayan and Yoruba systems: 2 digits

Sexagesimal52base 60; Babylonian, and still how an hour and a circle are divided: 1 digit

Balanced ternary1T0T1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary1110100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00110100

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 22 trailing zeros

Power of twoNo

Bytes134

Gray code101110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

8-bit00110100

16-bit0000000000110100

32-bit00000000000000000000000000110100

64-bit0000000000000000000000000000000000000000000000000000000000110100

One's complement11001011at 8 bits, every bit flipped

Bits reversed00101100at 8 bits

Rotated left by 101101000at 8 bits, wrapping

Shifted left by 11101000= 104, no wrap

Shifted right by 111010= 26, discarding the low bit

These bits as a double2.56914136 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime53+1

Previous prime47−5

Distance to nearest prime1

Nearest square below49

Nearest square above64

Powers & multiples

52 to the power 22,704

52 to the power 3140,608

52 to the power 47,311,616

52 to the power 5380,204,032

First ten multiples52, 104, 156, 208, 260, 312, 364, 416, 468, 520

Powers of twoBetween 2^5 (32) and 2^6 (64)

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 1

Divisible by 4Yes

Divisible by 5No, remainder 2

Divisible by 6No, remainder 4

Divisible by 7No, remainder 3

Divisible by 8No, remainder 4

Divisible by 9No, remainder 7

Divisible by 10No, remainder 2

Divisible by 11No, remainder 8

Divisible by 12No, remainder 4

Divisible by 100No, remainder 52

Collatz (3n + 1) trajectory

Steps to reach 111the total stopping time

Highest value reached52

Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven

First steps52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage5,200%

52% as a decimal0.52

52% of 10052

52% of 1,000520

As a fraction of 10052/100

Read another way

As seconds52 seconds

As bytes52 B

As a 24-bit colour#000034

Keep nerding

Every link below is a page Nerdulator can generate from what it already knows about this value.

52