Recognised as Number

47,736

Positive
Even
Composite
5 digits

47,736 is an even 5-digit integer and a composite number. It has 64 divisors and a digital root of 9.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value47,736

Digit count5

Digit sum27

Digit product3,528

Multiplicative persistence3times the digit product can be taken before one digit is left

Digital root9repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^3 × 3^3 × 13 × 17

Distinct prime factors42, 3, 13, 17

Number of divisors64

Sum of divisors σ(n)151,200

Aliquot sum103,464sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)13,824integers below n that share no factor with it

Carmichael function λ(n)144the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 13,824

Möbius function μ(n)0zero, because a prime divides n twice

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 8, 9, 12, 13, 17, 18, 24, 26, 27, 34, 36, 39, 51, 52, 54, 68, 72, 78, 102, 104, 108, 117, 136, 153, 156, 204, 216, 221, 234, 306, 312, 351, 408, 442, 459, 468, 612, 663, 702, 884, 918, 936, 1,224, 1,326, 1,404, 1,768, 1,836, 1,989, 2,652, 2,808, 3,672, 3,978, 5,304, 5,967, 7,956, 11,934, 15,912, 23,868, 47,73664 in total

Arithmetic

Previous number47,735

Next number47,737

Double95,472

Half23,868

Square2,278,725,696

Cube108,777,249,824,256

Square root218.485697472≈irrational, shown to 9 decimal places

Cube root36.275661576≈

Negation-47,736

Reciprocal0.0000209486≈

Representations

Decimal47,736

Binary101110100111100016 bits

Octal135170

HexadecimalBA78

Base 3610U0

Roman numeralNot defined above 3,999there is no agreed standard notation

In wordsforty-seven thousand, seven hundred and thirty-six

Ordinalforty-seven thousand, seven hundred and thirty-sixth

Scientific notation4.7736 × 10^4

Engineering notation47.736 × 10^3

In other bases

Ternary2102111000base 3; the most digit-efficient integer base after e: 10 digits

Quinary3011421base 5; one hand: 7 digits

Septenary256113base 7: 6 digits

Nonary72430base 9; each digit is two ternary digits: 5 digits

Duodecimal23760base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal5j6gbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal13:15:36base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T11T111000digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11100111110001000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1011101001111000

Bit length16 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits7within that length

Bit parityodd9 set bits, so odd; not the same as the number itself being even

Highest set bitbit 15worth 32,768

Lowest set bitbit 33 trailing zeros

Power of twoNo

Bytes2ba 78

Gray code1110011101000100n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1011101001111000

32-bit00000000000000001011101001111000

64-bit0000000000000000000000000000000000000000000000001011101001111000

One's complement0100010110000111at 16 bits, every bit flipped

Bits reversed0001111001011101at 16 bits

Rotated left by 10111010011110001at 16 bits, wrapping

Shifted left by 110111010011110000= 95,472, no wrap

Shifted right by 1101110100111100= 23,868, discarding the low bit

These bits as a double2.35847177 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime47,737+1

Previous prime47,717−19

Distance to nearest prime1

Nearest square below47,524

Nearest square above47,961

Powers & multiples

47,736 to the power 22,278,725,696

47,736 to the power 3108,777,249,824,256

47,736 to the power 45,192,590,797,610,684,416

47,736 to the power 5247,873,514,314,743,631,282,176

First ten multiples47,736, 95,472, 143,208, 190,944, 238,680, 286,416, 334,152, 381,888, 429,624, 477,360

Powers of twoBetween 2^15 (32,768) and 2^16 (65,536)

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5No, remainder 1

Divisible by 6Yes

Divisible by 7No, remainder 3

Divisible by 8Yes

Divisible by 9Yes

Divisible by 10No, remainder 6

Divisible by 11No, remainder 7

Divisible by 12Yes

Divisible by 100No, remainder 36

Collatz (3n + 1) trajectory

Steps to reach 1145the total stopping time

Highest value reached60,4241× the starting value

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

First steps47,736 → 23,868 → 11,934 → 5,967 → 17,902 → 8,951 → 26,854 → 13,427 → 40,282 → 20,141 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,773,600%

47,736% as a decimal477.36

47,736% of 10047,736

47,736% of 1,000477,360

As a fraction of 10047,736/100

Read another way

As seconds13 hours, 15 minutes and 36 seconds

As bytes46.617 KiB

As a 24-bit colour#00BA78

Keep nerding

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