Recognised as Number

42,163

Positive
Odd
Composite
5 digits

42,163 is an odd 5-digit integer and a composite number. It has 4 divisors and a digital root of 7.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value42,163

Digit count5

Digit sum16

Digit product144

Multiplicative persistence3times 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 factorisation11 × 3,833

Distinct prime factors211, 3,833

Number of divisors4

Sum of divisors σ(n)46,008

Aliquot sum3,845sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)38,320integers below n that share no factor with it

Carmichael function λ(n)19,160the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 38,320

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

SquarefreeYesno repeated prime factor

All divisors1, 11, 3,833, 42,1634 in total

Arithmetic

Previous number42,162

Next number42,164

Double84,326

Half21,081.5

Square1,777,718,569

Cube74,953,948,024,747

Square root205.336309502≈irrational, shown to 9 decimal places

Cube root34.805176048≈

Negation-42,163

Reciprocal0.0000237175≈

Representations

Decimal42,163

Binary101001001011001116 bits

Octal122263

HexadecimalA4B3

Base 36WJ7

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

In wordsforty-two thousand, one hundred and sixty-three

Ordinalforty-two thousand, one hundred and sixty-third

Scientific notation4.2163 × 10^4

Engineering notation42.163 × 10^3

In other bases

Ternary2010211121base 3; the most digit-efficient integer base after e: 10 digits

Quinary2322123base 5; one hand: 7 digits

Septenary233632base 7: 6 digits

Nonary63747base 9; each digit is two ternary digits: 5 digits

Duodecimal20497base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal5583base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:42:43base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T0110TTTT1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11110010111110111base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1010010010110011

Bit length16 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits8within that length

Bit parityeven8 set bits, so even; not the same as the number itself being odd

Highest set bitbit 15worth 32,768

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes2a4 b3

Gray code1111011011101010n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1010010010110011

32-bit00000000000000001010010010110011

64-bit0000000000000000000000000000000000000000000000001010010010110011

One's complement0101101101001100at 16 bits, every bit flipped

Bits reversed1100110100100101at 16 bits

Rotated left by 10100100101100111at 16 bits, wrapping

Shifted left by 110100100101100110= 84,326, no wrap

Shifted right by 1101001001011001= 21,081, discarding the low bit

These bits as a double2.08312898 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime42,169+6

Previous prime42,157−6

Distance to nearest prime6

Nearest square below42,025

Nearest square above42,436

Powers & multiples

42,163 to the power 21,777,718,569

42,163 to the power 374,953,948,024,747

42,163 to the power 43,160,283,310,567,407,761

42,163 to the power 5133,247,025,223,453,613,427,043

First ten multiples42,163, 84,326, 126,489, 168,652, 210,815, 252,978, 295,141, 337,304, 379,467, 421,630

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 1

Divisible by 4No, remainder 3

Divisible by 5No, remainder 3

Divisible by 6No, remainder 1

Divisible by 7No, remainder 2

Divisible by 8No, remainder 3

Divisible by 9No, remainder 7

Divisible by 10No, remainder 3

Divisible by 11Yes

Divisible by 12No, remainder 7

Divisible by 100No, remainder 63

Collatz (3n + 1) trajectory

Steps to reach 1194the total stopping time

Highest value reached250,5045× the starting value

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

First steps42,163 → 126,490 → 63,245 → 189,736 → 94,868 → 47,434 → 23,717 → 71,152 → 35,576 → 17,788 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,216,300%

42,163% as a decimal421.63

42,163% of 10042,163

42,163% of 1,000421,630

As a fraction of 10042,163/100

Read another way

As seconds11 hours, 42 minutes and 43 seconds

As bytes41.175 KiB

As a 24-bit colour#00A4B3

Keep nerding

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