Recognised as Number

42,837

Positive
Odd
Composite
5 digits

42,837 is an odd 5-digit integer and a composite number. It has 8 divisors and a digital root of 6.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value42,837

Digit count5

Digit sum24

Digit product1,344

Multiplicative persistence4times 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 × 109 × 131

Distinct prime factors33, 109, 131

Number of divisors8

Sum of divisors σ(n)58,080

Aliquot sum15,243sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)28,080integers below n that share no factor with it

Carmichael function λ(n)7,020the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 28,080

Möbius function μ(n)−13 distinct prime factors, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 3, 109, 131, 327, 393, 14,279, 42,8378 in total

Arithmetic

Previous number42,836

Next number42,838

Double85,674

Half21,418.5

Square1,835,008,569

Cube78,606,262,070,253

Square root206.971012463≈irrational, shown to 9 decimal places

Cube root34.989656808≈

Negation-42,837

Reciprocal0.0000233443≈

Representations

Decimal42,837

Binary101001110101010116 bits

Octal123525

HexadecimalA755

Base 36X1X

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

In wordsforty-two thousand, eight hundred and thirty-seven

Ordinalforty-two thousand, eight hundred and thirty-seventh

Scientific notation4.2837 × 10^4

Engineering notation42.837 × 10^3

In other bases

Ternary2011202120base 3; the most digit-efficient integer base after e: 10 digits

Quinary2332322base 5; one hand: 7 digits

Septenary235614base 7: 6 digits

Nonary64676base 9; each digit is two ternary digits: 5 digits

Duodecimal20959base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal571hbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:53:57base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T1TTT10TT0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11111101101010101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1010011101010101

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 odd

Highest set bitbit 15worth 32,768

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes2a7 55

Gray code1111010011111111n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1010011101010101

32-bit00000000000000001010011101010101

64-bit0000000000000000000000000000000000000000000000001010011101010101

One's complement0101100010101010at 16 bits, every bit flipped

Bits reversed1010101011100101at 16 bits

Rotated left by 10100111010101011at 16 bits, wrapping

Shifted left by 110100111010101010= 85,674, no wrap

Shifted right by 1101001110101010= 21,418, discarding the low bit

These bits as a double2.11642901 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime42,839+2

Previous prime42,829−8

Distance to nearest prime2

Nearest square below42,436

Nearest square above42,849

Powers & multiples

42,837 to the power 21,835,008,569

42,837 to the power 378,606,262,070,253

42,837 to the power 43,367,256,448,303,427,761

42,837 to the power 5144,243,164,475,973,934,997,957

First ten multiples42,837, 85,674, 128,511, 171,348, 214,185, 257,022, 299,859, 342,696, 385,533, 428,370

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 1

Divisible by 5No, remainder 2

Divisible by 6No, remainder 3

Divisible by 7No, remainder 4

Divisible by 8No, remainder 5

Divisible by 9No, remainder 6

Divisible by 10No, remainder 7

Divisible by 11No, remainder 3

Divisible by 12No, remainder 9

Divisible by 100No, remainder 37

Collatz (3n + 1) trajectory

Steps to reach 175the total stopping time

Highest value reached128,5123× the starting value

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

First steps42,837 → 128,512 → 64,256 → 32,128 → 16,064 → 8,032 → 4,016 → 2,008 → 1,004 → 502 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,283,700%

42,837% as a decimal428.37

42,837% of 10042,837

42,837% of 1,000428,370

As a fraction of 10042,837/100

Read another way

As seconds11 hours, 53 minutes and 57 seconds

As bytes41.833 KiB

As a 24-bit colour#00A755

Keep nerding

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