Recognised as Number

51

Positive
Odd
Composite
2 digits

51 is an odd 2-digit integer and a composite number. It has 4 divisors and a digital root of 6.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value51

Digit count2

Digit sum6

Digit product5

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 numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation3 × 17

Distinct prime factors23, 17

Number of divisors4

Sum of divisors σ(n)72

Aliquot sum21sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)32integers below n that share no factor with it

Carmichael function λ(n)16the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 32

Möbius function μ(n)+12 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 3, 17, 514 in total

Arithmetic

Previous number50

Next number52

Double102

Half25.5

Square2,601

Cube132,651

Square root7.141428429≈irrational, shown to 9 decimal places

Cube root3.708429769≈

Negation-51

Reciprocal0.0196078431≈

51 factorial1551118753287382280224243016469303211063… (67 digits)

Representations

Decimal51

Binary1100116 bits

Octal63

Hexadecimal33

Base 361F

Roman numeralLI

In wordsfifty-one

Ordinalfifty-first

Scientific notation5.1 × 10^1

Engineering notation51

In other bases

Ternary1220base 3; the most digit-efficient integer base after e: 4 digits

Quinary201base 5; one hand: 3 digits

Septenary102base 7: 3 digits

Nonary56base 9; each digit is two ternary digits: 2 digits

Duodecimal43base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 2 digits

Vigesimal2bbase 20; hands and feet, and the Mayan and Yoruba systems: 2 digits

Sexagesimal51base 60; Babylonian, and still how an hour and a circle are divided: 1 digit

Balanced ternary1T0T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary1110111base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00110011

Bit length6 bitsto write the magnitude

Set bits4the population count, or Hamming weight

Zero bits2within that length

Bit parityeven4 set bits, so even; not the same as the number itself being odd

Highest set bitbit 5worth 32

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes133

Gray code101010n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

8-bit00110011

16-bit0000000000110011

32-bit00000000000000000000000000110011

64-bit0000000000000000000000000000000000000000000000000000000000110011

One's complement11001100at 8 bits, every bit flipped

Bits reversed11001100at 8 bits

Rotated left by 101100110at 8 bits, wrapping

Shifted left by 11100110= 102, no wrap

Shifted right by 111001= 25, discarding the low bit

These bits as a double2.51973479 × 10^-322≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime53+2

Previous prime47−4

Distance to nearest prime2

Nearest square below49

Nearest square above64

Powers & multiples

51 to the power 22,601

51 to the power 3132,651

51 to the power 46,765,201

51 to the power 5345,025,251

First ten multiples51, 102, 153, 204, 255, 306, 357, 408, 459, 510

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 3

Divisible by 5No, remainder 1

Divisible by 6No, remainder 3

Divisible by 7No, remainder 2

Divisible by 8No, remainder 3

Divisible by 9No, remainder 6

Divisible by 10No, remainder 1

Divisible by 11No, remainder 7

Divisible by 12No, remainder 3

Divisible by 100No, remainder 51

Collatz (3n + 1) trajectory

Steps to reach 124the total stopping time

Highest value reached2324× the starting value

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

First steps51 → 154 → 77 → 232 → 116 → 58 → 29 → 88 → 44 → 22 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage5,100%

51% as a decimal0.51

51% of 10051

51% of 1,000510

As a fraction of 10051/100

Read another way

As seconds51 seconds

As bytes51 B

As a 24-bit colour#000033

Keep nerding

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

51