Recognised as Number

42,313

Positive
Odd
Composite
5 digits

42,313 is an odd 5-digit integer and a composite number. It has 8 divisors and a digital root of 4.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value42,313

Digit count5

Digit sum13

Digit product72

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

Digital root4repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation17 × 19 × 131

Distinct prime factors317, 19, 131

Number of divisors8

Sum of divisors σ(n)47,520

Aliquot sum5,207sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)37,440integers below n that share no factor with it

Carmichael function λ(n)9,360the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 37,440

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

SquarefreeYesno repeated prime factor

All divisors1, 17, 19, 131, 323, 2,227, 2,489, 42,3138 in total

Arithmetic

Previous number42,312

Next number42,314

Double84,626

Half21,156.5

Square1,790,389,969

Cube75,756,770,758,297

Square root205.701239666≈irrational, shown to 9 decimal places

Cube root34.846401747≈

Negation-42,313

Reciprocal0.0000236334≈

Representations

Decimal42,313

Binary101001010100100116 bits

Octal122511

HexadecimalA549

Base 36WND

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

In wordsforty-two thousand, three hundred and thirteen

Ordinalforty-two thousand, three hundred and thirteenth

Scientific notation4.2313 × 10^4

Engineering notation42.313 × 10^3

In other bases

Ternary2011001011base 3; the most digit-efficient integer base after e: 10 digits

Quinary2323223base 5; one hand: 7 digits

Septenary234235base 7: 6 digits

Nonary64034base 9; each digit is two ternary digits: 5 digits

Duodecimal205a1base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal55fdbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:45:13base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T011001011digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11110010101011001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1010010101001001

Bit length16 bitsto write the magnitude

Set bits7the population count, or Hamming weight

Zero bits9within that length

Bit parityodd7 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

Bytes2a5 49

Gray code1111011111101101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1010010101001001

32-bit00000000000000001010010101001001

64-bit0000000000000000000000000000000000000000000000001010010101001001

One's complement0101101010110110at 16 bits, every bit flipped

Bits reversed1001001010100101at 16 bits

Rotated left by 10100101010010011at 16 bits, wrapping

Shifted left by 110100101010010010= 84,626, no wrap

Shifted right by 1101001010100100= 21,156, discarding the low bit

These bits as a double2.09053997 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime42,323+10

Previous prime42,307−6

Distance to nearest prime6

Nearest square below42,025

Nearest square above42,436

Powers & multiples

42,313 to the power 21,790,389,969

42,313 to the power 375,756,770,758,297

42,313 to the power 43,205,496,241,095,820,961

42,313 to the power 5135,634,162,449,487,472,322,793

First ten multiples42,313, 84,626, 126,939, 169,252, 211,565, 253,878, 296,191, 338,504, 380,817, 423,130

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 1

Divisible by 5No, remainder 3

Divisible by 6No, remainder 1

Divisible by 7No, remainder 5

Divisible by 8No, remainder 1

Divisible by 9No, remainder 4

Divisible by 10No, remainder 3

Divisible by 11No, remainder 7

Divisible by 12No, remainder 1

Divisible by 100No, remainder 13

Collatz (3n + 1) trajectory

Steps to reach 180the total stopping time

Highest value reached214,2165× the starting value

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

First steps42,313 → 126,940 → 63,470 → 31,735 → 95,206 → 47,603 → 142,810 → 71,405 → 214,216 → 107,108 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,231,300%

42,313% as a decimal423.13

42,313% of 10042,313

42,313% of 1,000423,130

As a fraction of 10042,313/100

Read another way

As seconds11 hours, 45 minutes and 13 seconds

As bytes41.321 KiB

As a 24-bit colour#00A549

Keep nerding

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